Question

In Khan Academy: Equations & inequalities word problems:

A 5 inch by 7 inch picture is placed in a frame that creates a uniform border of x inches around the picture.
The area of the entire frame (including where the picture is placed is equal to 120 square inches.

Answer 1

Answer ( if trying to find x ) :

x = 44

Explanation:

5 x 7 = 35 ( area of picture )

120 -> ( area of the whole picture + frame )

120 - 35 = 85 ( area of just the frame )

factor's of 85 -> 1 ,5 ,17 ,85 ( can't be 1 by 85 inch's picture ,so you get 5 by 17 )

5 + 5 + 17 + 17 = 44 (perimeter of the frame ( perimeter formula= l + l + w + w ) )

44 inch's ( ? )

Answer 2

(7+2x)(5+2x)=120

Explanation:

We know that the picture is 5 inches wide and 7 inches long. Since there is a uniform border of x inches around the picture, we must add 2x inches to each dimension.

Therefore, the width of the frame is 5+2x, and the length of the frame is 7+2x