Question

A rectangular photo has a frame that is 1 inch wide. If the photo is twice as long as it is wide and the area of the photo and frame together is 60 inches, what are the dimensions of the photo?

Answer 1

Answer: the length is 8 inches

The with is 4 inches

Step-by-step explanation:

Let L represent the length of the photo.

Let W represent the width of the photo.

If the photo is twice as long as it is wide, it means that

L = 2W

The rectangular photo has a frame that is 1 inch wide. This means that

The length of the photo and the frame is L + 2

The width of the photo and the frame is W + 2

If the area of the photo and frame together is 60 inches², it means that

(L + 2)(W + 2) = 60 - - - - - - - - - - -1

Substituting L = 2W into equation 1, it becomes

(2W + 2)(W + 2) = 60

2W² + 4W + 2W + 4 = 60

2W² + 6W + 4 - 60 = 0

2W² + 6W - 56 = 0

Dividing through by 2, it becomes

W² + 3W - 28 = 0

W² + 7W - 4W - 28 = 0

W(W + 7) - 4(W + 7) = 0

(W - 4)(W + 7) = 0

W = 4 or W = - 7

The width cannot be negative , therefore, W = 4

Substituting W = 4 into L = 2W, ut becomes

L = 2 × 4 = 8 inches