Question

An art class plans to paint part of a rectangular wall in the cafeteria and leav the rest of the wall white, as shown. The painted section will take 2/3 of the area of the wall. What is the value of x?

Answer 1

11 ft

Explanation:

First, let's find the entire area of the wall.

so

10ft x 33ft = 330 ft^2

We know that only 2/3 of the wall was painted so

2/3 x 330 ft^2 = 220ft^2

We can break apart the shapes of the wall into a square and a triangle, which will allow. Then we can find the area of each using x as our unknown.

Square area = 10x

Triangle area = (10(33-x))/2 same as ((330-10x)/2) = 165 - 5x

square area + triangle area = 10x + 165 -5x = 5x + 165 (the painted wall)

We know the actual area and the area of the wall with the unknown x, so now we can set them equal to each other.

165+5x = 220

5x = 55

x = 11