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Down. A right rectangular prism with a length of 12 m, a width of 5 m, and a height of 8 m.(FIGURE CAN'T COPY)....

Question

Down. A right rectangular prism with a length of 12 m, a width of 5 m, and a height of 8 m.(FIGURE CAN'T COPY).

Down. A right rectangular prism with a length of 12 m, a width of 5 m, and a height of 8 m. (FIGURE CAN'T COPY).



Answers

The rectangle shown here has an area of $8 \mathrm{m}^{2} .$ Find the width. (RECTANGLE CANNOT COPY)

Find the height of a right rectangular prison with surface area, 286 square meters, a length of 10 meters and a width of eight meters. So to do this, we're going to use the formula for the surface area of a rectangular prism. Substitute the values we know and simplify until we have the unknown value for a tight. We know that the surface area of a rectangular prism is equal to the perimeter of the base times height, plus twice the area of the base. Now keep in mind that the area of the base is length times width, so we can use our length and width that are given to substitute in. For B. The perimeter is equal to 10 less eight plus 10 plus eight the perimeter of the base, and that is 36. Oh, substituting these values the 286 for our surface area. The perimeter is 36. We do not know h. That's what we need to find, plus two times the length times the width 286 equals 36 h plus 160 now simplify or isolate the variable for the height. That's what we need to do next. Subtract 1 60 from both sides. That'll leave us with 126 is equal to 36 h divide both sides by 36 and we have HH equals 3.5. The height of the rectangular prism is 3.5 meters.

So you can have to get your your arm ruler out for this. And what you want to do is measure G on. Wait in which and height, right. Um and then the diagonal, It's just found from segment there. So diagonal, square, root of length, squirt close, the wit squared, plus the height squared. And then just when you see that box, you just kind of got to realize what's what, and you can label them anything you want. But one of these dimensions is gonna be the height. Um, and one is the width and want us the length spends just basically how you want full it, Right. So this is what's on your paper and you can leave what anything you want. But I would kind of fold up the box like take this piece and come per over there like, folded up top. So if I were measuring it, I would probably say that this was the height. And then from here to here would be the length. And then from here to here be the wit

Alright, so I've got the dimensions written down here in the box. So late. 12 with eight height. Six. Right. And we have to figure out what is the length of the Dagnall of the rectangular prism that's defined by these is most closely 6 44 15 or to 44 meters. So let's figure out we can cross out. It's just not gonna be possible for the 2 44 to fit in a box of these mentions. I mean, that's just like you connive all that. It's not gonna happen. 44 is the same thing. So this is a contest between six and 15? Um, they have 6.6 and 15 so the distance during the diagonal along diagonal is the square of six squared, plus eight squared plus 12 squared. You do that calculation and I calculate to be 15.6 meters

We need to find the surface area of a rectangular prism that has a length that is three times. It's with a height that is twice its with in a lateral area that is 144 centimeters squared. So let's start first by figuring out what the witness. We could do this by setting up the equation for the lateral area. You know, the lateral area is equal to the perimeter times the height. The perimeter is equal to two times the length plus the width. We know that the length is equal to three times the width, so if we substitute those values in and the height is twice the width we can solve for W 144 is our lateral area is equal to twice the length of www plus the width times the height of two W. So 144 is equal to two times four W times to W. Two times four times two is 16 W. TIMES W is w squared to solve For w Let's first divide both sides by 16 and 144 divided by 16 is nine is equal to the width squared. Take the square root of both sides and we have a width of three centimeters. Now we confined the dimensions for the length and height. If our with is three, our length is three times three and our height is two times three. So, clearly my picture is not drawn to scale. These were all centimeters. Never forget your units. Now we confined the service area. We know that the surface area is equal to the lateral area, plus twice the area of the base. The area of the base is three by nine, which is 27. So we can substitute our values. Lateral areas 144 plus two times 27. This gives us 144 plus 54 for a total surface area of 198 square centimeters.


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