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# a room with width, length,and height with four walls needs to be painted.

a.write a formula for the area that needs to be painted not accounting for doors or windows
b.rewrite the formula to find h in terms of area,length, and width
c.if length is 18 ft,width is 14 ft and area is 512 ft2, what is the height of the room?
d.suppose length is equal to width.write a formula for area in terms of width and height.

### 1 Answer by Expert Tutors

Jason T. | Jason Tutors Math & PhysicsJason Tutors Math & Physics
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All the walls have the same height. Two of the walls will span a distance equal to the length and their areas will be l*h. Two of the walls will span a distance of the width, and their areas with be w*h.

a) Total area = 2(l*h) + 2(w*h) = 2h(l+w)

b) start with A = 2h(l+w). Isolate h, since that is what you want to find.
Get rid of the 2 by dividing each side by 2
Get ride of the (l+w) by dividing each side by (l+w)

c) Use your expression for h found in step b) and substitute the given values in for A, l, and w

d) We need a formula for the area, A. In step b), A = 2h(l+w). If l=w and we want to write the equation for A with only width and height, we get rid of l. Let's rewrite l as w, since l=w.

A = 2h(w+w)

w+w=2w, so A = 2h(2w) = 4hw, so A=4hw