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The width of a painting is 4 inches less than the length. The frame that surrounds the painting is 2 inches wide and has an area of 240 square inches. What are the dimensions of the painting? (Hint: The total area minus the area of the painting alone is equal to the area of the frame.)

Sagot :

Raphealnwobiidn

Answer:

131 in²

Step-by-step explanation:

Let x represent the length of the painting. Given that The width of a painting is 4 inches less than the length. Hence:

Width = x - 4

The area of painting = length * width = x(x - 4) = x² - 4x

The frame that surrounds the painting is 2 inches wide (at the top and bottom, left and right). Hence the total width of the frame = (x - 4) + 2 + 2 = x, the length of the frame = x + 2 + 2 = x + 4

The area of the frame = length * breath = x(x +  4) = x² + 4x

Given that the area of the frame = 240 in², hence:

x² + 4x = 240

x² + 4x - 240 = 0

x = -17.62 and x = 13.62

Since the length cannot be negative, hence length = x = 13.62 inches

Area of painting = x(x - 4) = 13.62(13.62 - 4) = 131 in²

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