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
