Carcass wrote:
In the figure shown above, line segment QR has length 12, and rectangle MPQT is a square. If the area of rectangular region MPRS is 540, what is the area of rectangular region TQRS?
(A) 144
(B) 216
(C) 324
(D) 360
(E) 396
Add the given information...
Let x = the length of each side of square MPQT
GIVEN: The area of rectangular region MPRS is 540In other words:
(base)(height) = 540Substitute values to get: (x + 12)(x) = 540
Expand: x² + 12x = 540
Set equal to zero: x² + 12x - 540 = 0
Factor: (x + 30)(x - 18) = 0
So, EITHER x = -30 OR x = 18
Since the length cannot be negative, it must be the case that
x = 18 What is the area of rectangular region TQRS? Area = (base)(height) = (12)(18) = 216
Answer: B
Cheers,
Brent