A picture frame has a length l = 11 inches and a height h = 8 inches (see figure). If the frame width is x inches, write an expression for the display area of the frame. A) x² - 19x + 88 in² B) 88 in² C) 4x² - 38x + 88 in² D) x² - 88 in²

Question

Quizplus · Accepted Answer

The display area of the frame can be found by subtracting the area of the inner rectangle (which is the area of the picture) from the area of the outer rectangle. The area of the inner rectangle is (l - 2x) * (h - 2x), and the area of the outer rectangle is lh. Therefore, the display area is:

display area = lh - (l - 2x)(h - 2x)
display area = lh - (lh - 2lx - 2hx + 4x^2)
display area = 4x^2 - 2lx - 2hx + lh
display area = 4x^2 - 22x + 88

So the expression for the display area of the frame is 4x^2 - 22x + 88. Therefore, the correct answer is choice C.

A Picture Frame Has a Length L = 11 Inches