Transcript The figure above shows a square region divided into four rectangular regions, three of which have areas 5x, 5x, and x²,

The figure above shows a square region divided into four rectangular regions, three of
which have areas 5x, 5x, and x², respectively. If the area of MNOP is 64, what is the
area of square QROS ?
(a) 9
(b) 25
(c) 30
(d) 34
(e) 39
Correct Answer: B
Explanation:
Since MNOP and QROS are squares, MN = NO = 8 and QR = RO. Thus, MU = NR
and the rectangle with area x² must be a square with sides of length x. The rectangles
with area 5x must have sides of length x and 5. Thus, the area of QROS is equal to 5²
= 25.
Another approach is the following. Since QROS is a square, QR = RO. Thus, MU =
NR and MUQT is a square with sides of length x. The rectangles with area 5x must
have sides of length x and 5. Since the area of MNOP is 64:
(x + 5)² = 64
x² + 5x + 5x + 25 = 64
Thus, the area of QROS is 25.