2011 AMC 10B Problem 14

Question

A rectangular parking lot has a diagonal of

25

meters and an area of

168

square meters. In meters, what is the perimeter of the parking lot?

52

58

62

68

70

Let the side lengths be

x

and

y

Use

(x+y)^2=x^2+y^2+2xy

Let the side lengths be

l,w.

We wish to find

2(l+w).

From the Pythagorean Theorem, we get

25 = \sqrt{l^2+w^2}

l^2+w^2 = 625

We also know

lw = 168.

As such

\begin{aligned}l^2+2lw+ w^2 &= (l+w)^2 \\&= 961 \\&= 31^2.\end{aligned}

This makes

l+w = 31,

and as such, our answer is

31\cdot 2=62.

Thus, the correct answer is C .

Problem 14 in other years