Problem Solving

In the figure above, the length of the large rectangle is 12 inches and the width of the large rectangle is 10 inches. The area of the unshaded rectangle is equal to the area of the shaded region. If the ratio of the length to the width of the unshaded rectangle is equal to the ratio of the length to the width of the large rectangle, what is the length of the unshaded rectangle, in inches?[/img]


-Answer says that "the area of the unshaded rectangle is of 120 square inches" Q: how do we know that?

The area of the unshaded rectangle = area of shaded region => 120/2 = 60

L:B = 12:10 = 6:5

The answer should be 6sqrt(2)

xy = 12(10-y) + y(12-x)

solve for xy to get xy = 60. So area of unshaded rectangle is 60 not 120.

then we know that

x/y = 12/10 = 6/5

so 5x = 6y

substitute into xy = 60, to get (5x/6)*x = 60

solve for x to get sqrt(72) or 6sqrt(2)

Agree with Prindaroy.

it just came to me what "the area of shaded region is equal to the area of the unshaded region" means... (what an idiot!) thank u all for the quick posts.