Question

Gretchen is building a picture frame. The frame around the picture is k inches longer than it is wide as shown in the picture. The shaded border is 2 inches wide and has an area of (a) Write and solve an equation that will enable you to find out the value of k.

A. k - 2 = a
B. k = a + 2
C. k^2 - 2a = 0
D. 2k - a = 0

Answer 1

To find the value of k, write and solve an equation based on the given information. Assume the width of the picture is x inches. The width of the larger square is 2x inches, and the length is 2x + k inches.

Step-by-step explanation:

To find the value of k, we need to write and solve an equation based on the given information. The frame around the picture is k inches longer than it is wide. Since the shaded border is 2 inches wide, the dimensions of the larger square (frame + border) are twice the dimensions of the smaller square (picture).

Let's assume the width of the picture is x inches. The width of the larger square is then 2x inches.

The length of the larger square is k inches longer than its width, so it is 2x + k inches long.

The area of the shaded border is given as a. The difference between the areas of the larger square and the smaller square is equal to the area of the shaded border. Therefore, we can write the equation:

(2x + k)^2 - x^2 = a

Simplifying this equation will give us the value of k.