Question

(Worth 16 pts!) what lengths could I use to make this prism have a surface area of 200!?

Answer 1

5 by 5 by 7.5

Explanation:

The surface area of a rectangular prism is given by the formula ...

A = 2(LW +H(L +W)

__

There are many ways to choose L, W, and H to give the desired area. One way is to arbitrarily choose L = W = 5, then we have ...

200 = 2(5·5 +H(5 +5))

200 = 20H +50 . . . . . . . simplify

150 = 20H . . . . . subtract 50

H = 7.5 . . . . . . divide by 20

Possible dimensions are ...

5 by 5 by 7.5

Answer 2

5 by 5 by 7.5

Explanation:

The surface area of a rectangular prism is given by the formula ...

A = 2(LW +H(L +W)

__

There are many ways to choose L, W, and H to give the desired area. One way is to arbitrarily choose L = W = 5, then we have ...

200 = 2(5·5 +H(5 +5))

200 = 20H +50 . . . . . . . simplify

150 = 20H . . . . . subtract 50

H = 7.5 . . . . . . divide by 20

Possible dimensions are ...

5 by 5 by 7.5