Answer:
The height of the picture is 3 inches.
Step-by-step explanation:
A picture frame goes around a picture such that it has 1 inch thickness. The width of the picture is 4 inches more than twice the height.
Therefore, our picture has the dimensions of height = h and width = 4 + 2h.
The area of the the frame and picture is 60 square inches. Thus, the picture frame with the picture's dimension is height (picture frame) =height of the picture + 2 (1 inch per side) and the width = width of the picture + 2 (1 inch per side).
Area = height x width
60 = (h +2) (4+ 2h + 2)
60 = (h+ 2) (2h + 6)
60 = 2h² + 6h + 4h + 12, combine like terms
2h² + 10h - 48 = 0, divide the whole equation by 2 to simplify
h² + 5h -24 = 0, factor the equation
(h+ 8)(h-3) = 0
h+8 = 0, h -3=0
h = - 8 and h = 3, since there is no negative height therefore the height is 3 inches.
