Question

The area if a rectangular frame is 32 square inches. The perimeter of the frame is 24 inches. Which shows the correct dimensions of the frame?

Answer 1

8 x 4

Explanation:

Lets say the length is x and the width is y.

xy = 32

2x + 2y = 24

Rearranging the second equation, we get:

2x = 24 - 2y

/2 /2

x = 12 - y

substitute into the first equation

y(12 - y) = 32

12y - y^2 = 32

-32 -32

-y^2 +12y - 32 = 0

x -1 x -1

y^2 - 12y + 32 = 0

(y - 8)(y - 4) = 0

y = 8 or 4

substitute into x = 12 - y.

x = 12 - 8 = 4

x = 12 -4 = 8

so the correct dimensions are 4 x 8, as either x = 4 and y =8, or x = 8 and y = 4.

Hope I helped!