Question

The surface area (SA) of a rectangular prism can be determined by using the formula, where l = length, w = width, and h = height.

Answer 1

Step-by-step explanation

We must solve for h the following equation:

`SA=2\cdot(l\cdot w+l\cdot h+h\cdot w).`

(1) We divide both sides by 2:

`l\cdot w+l\cdot h+h\cdot w=(SA)/(2).`

(2) We pass the term lw on the left side as -lw on the right side:

`l\cdot h+h\cdot w=(SA)/(2)-l\cdot w.`

(3) We take h as a common factor on the left:

`h\cdot(l+w)=(SA)/(2)-l\cdot w.`

(4) Finally, we divide both sides by (l + w):

`h=((SA)/(2)-l\cdot w)/(l+w)=(SA)/(2(l+w))-(lw)/(l+w).`Answer
`h=(SA)/(2(l+w))-(lw)/(l+w)`