5

9 1 H 1 3 Tnete 1 There [s only 5ej are nC L H The measurements for Ihe coltuci cnoicu Cz120" 1 Ino 2iu) 3/015500 1 on0 possible yun solutlons solulon thoa...

Question

9 1 H 1 3 Tnete 1 There [s only 5ej are nC L H The measurements for Ihe coltuci cnoicu Cz120" 1 Ino 2iu) 3/015500 1 on0 possible yun solutlons solulon thoausonsio0 L Suluuum 1 for this triangle HH L 1 { uiangle side 1 0 ane bare hand 1 follows Iolla comiplulu Vau choicu Arauno 8 cubiu 1 1 1 placera M o Solvu . 1 net 1

9 1 H 1 3 Tnete 1 There [s only 5ej are nC L H The measurements for Ihe coltuci cnoicu Cz120" 1 Ino 2iu) 3/015500 1 on0 possible yun solutlons solulon thoausonsio0 L Suluuum 1 for this triangle HH L 1 { uiangle side 1 0 ane bare hand 1 follows Iolla comiplulu Vau choicu Arauno 8 cubiu 1 1 1 placera M o Solvu . 1 net 1



Answers

Look at the right triangle below. Which of the following could be the triangle's dimensions? (FIGURE CAN'T COPY). F. 9 G. $9 \sqrt{2}$ H. $18 \sqrt{2}$ J. 36

In description as of one is a regular hexagon circumscribing a circle. So here you can see that to the figure. So it is a regular has gone which is inscribed in the circle, suppose the radius of circle which is our. So here earliest of circle. No, here you can see that it is also Leaders of circle which is E. And O. P. Is a right is off circle And it is a regular has gone. So angle will be 60, 60 and 60, so it will be equilateral triangle. So here we know that also are equal. So here that side will be our which is E. To the Ecuador triangle. We can get the area of regular has gone which is as someone equal to sorry, except to equal to. So here you can see that in this regard total six a coral triangle. So They all are same. So we multiply by six time A. of the coral triangle, which is squared 3.4 times all square equal to three times Square root three times are square up on two. Now we have to find the audio ads of one. So here you can see that regular has gone some circumscribing a circle. So here you can see that radius of circles which is our it's okay you can see that it is a little triangle. So that angle will be 60°. And here mm That angle half of 60s. So here we get 30 degree suppose that side will be X. To the diplomatic property. And here we use Hussein dang tita equal to ex upon our. and here the value of tree to which is 30°. So now here 10 30° equal to ex upon our the value of 10 30 which is one of one square or three. So you can write like that X. Equal to three. Sorry are upon square or three. Now you can see that the side of hexagon which is two X. And here the value of X is our upon its quality. So you can write like that sidle hexagon equal to two times are upon square all three. So now we know that the area of hexagon for at someone area equal to 16 Squad of 3.4 times side which is two times are upon Square 3 to the power to now we simplify this. So here we get three times square three upon do time four times r squared up on three equal to four times square or three times are square upon to. So here we get to times square or three times artist. So now we have to find the ratio of a. of s. of one upon A. R. S. A. two equal to To Times Square three times are square upon three times square, or three upon do times are square. So here we get 4.3. So ratio will be four racial 3. It is a final answer, which is options first.

Question asked us to find the base of this triangle when we're given the height as this. And what we need to remember is that to find the area of a triangle, we have to multiply 1/2 times base times height. So we're gonna plug in the information that we have. So for a were given that the area is six h cubed plus three h squared less each and we're trying to solve for B. But the each that they give us the height is just each and just like a normal equation. When we're trying to solve for a variable in this case, E, we have to isolate it. So the first thing that we can do to isolate is to divide both sides of the equation by h so we can rewrite the left hand side as six h cubed over each plus three h squared over age plus h over each equals 1/2 be. And we just have to remember that when we are dividing variables that have exponents, we need to subtract their exponents. So for this first, uh, term three minus one gives us too. So that tells us that our first term will simplify to six h squared and for the second term to minus one gives us one. So that tells us we're just left with three h. And for this last term, since it's the same thing in the numerator and the denominator, this entire thing just simplifies toe one, and we're going to bring over our right hand side. And now to isolate be, we can multiply both sides of the equation by two. And when we do that, our 1/2 will cancel. And now we can just distribute this, too to each term on the left hand side. So six h squared times two gives us 12 each squared reach times two gives us six h and one times two is just too. And that is what B is equal to.

So in the during question, we have a triangle just given us photos. So incredible has sites six, 14 and 16 and the height of the triangle is given us 323 minutes. No, we are told to find the area of the grand jury so any of the country can be found. You see the formula half big age, which is half times the length of base times the height of the trend. So half times 16 times 33 use this 24 as well as the area of the tragedy 24 times Route three is equal to 41 point 57 squared Urals. So this is the idea of the given trend. Now let's verify this area using the heron's formula. So according to Heron's formula, we can find you can find the area of did you and Triangle. Using the phone under the square root of s times as minus eight times as minus big times is my necessary. Where a BNC are the length of the triangle and s is equal to a plus B plus C divided by two. So let a equal to six equal to 14 and C equal to 16. So then we can write. S is equal to six plus 14 plus 16 he wanted by two which is equal to the six plus 14 is 2020 plus 16 is 36 26 divided by two is 18. So s is equal to 18. So 18 times 18 minus a six times 18 minus B which is 14 and then 18 minus C, which is 16. So this is equal to 18 times 18. Minus six is 12, 18, minus 14, 4 and 18 minus 16 is too. So the idea is equal to the square root of 18 times. 18 times, 12 times, four times two. Excuse us. The answer. A square root of 1007 between the eight, which gives us the value 41.57 square units. So hence we have 85. That Heron's formula uses the same area as that of the formula which we used ever, which is half beach. So I hope you understood the method. Can you

So in the given question, we have a triangle in which the length of sites are given as 6, 14 and then, and the height of the triangle is given us 33 humans, three or three humans. So let's find the area of the strangle. The area of the strangle can be found as half village, which is half times length of base of the grand jury times height of the triangle, which means the area is equal to or above 10 times three room dream, which is equal to 15 to drink. So 15 Group three gives us a value of 25.9, which is approximately equal to 26 square units. And so this is what we obtain using the 4.5 beach. Now let's use herons for love to find the area of the client. So according to her own form, now the area of a triangle can be found. Music the form love square root of as times as minus eight times as minus B times as minus C, an, A, B and C and the length of signs of the Triangle and s. The sequel tune a plus B plus C divided by two. So let a B six b equal to 14 and C equal to 10. Then we can take s is equal to six plus 14 plus 10 divided by two which is equal to 30 limit by two excuses The value of S s in right, so we can substitute these values over here. So 15 times 15 minus six times 15 minus 14 times 15 minus 10, which is equal to square root of 15 times 15 minus six is within 86 this canyon. Thanks. 15 minutes for Penis. One times 15 minus 10 is framed. So even get the man U square root off 15 times nine and five, which is equal to root of 6 75 And I'm taking the square root of 6 75. Begin the answer US 26. 25 point iron, which is approximately equal to 26 square units. Just as we found the idea using the above for minorities, half beans. So hence we can say that Harold from love. Here's the idea, uh, as the same as that of the formula Half beach. So I hope you understood the method. Thank you


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