Rectangular canvas picture

Question

(1 point) A rectangular canvas picture measures 8 inches by 10 inches. The canvas is mounted inside a frame of uniform width, increasing the total area covered by both canvas and frame to 120 square inches. Find the uniform width of the frame.

Answer 1

Let w is the uniform width of the frame.

If the canvas is 8 x 10 inches, then

                   (8+2w) x (10 + 2w) is the size of the frame.

 

We calculate the area of the frame using formula for area of rectangle (A = l•w)

                    A = l•w

                    120 = (8+2w) • (10 + 2w)

                    120 = 80 + 16 w + 20 w + 4 w²

                    120 = 80 + 39w + 4w²

                     4w²+36w-40=0                       (To simplify, we divide the equation by 4)

                       w²+9w -10=0

 

We use quadratic formula or factoring to solve this equation. It has two solutions w₁=-10 and w₂=1.

The only possible value for the width is 1 inch.

 

The uniform width is 1 inch.