2011 AMC 10B Problems/Problem 14

Revision as of 19:50, 25 May 2011 by Gina (talk | contribs) (Created page with '== Problem 14 == A rectangular parking lot has a diagonal of <math>25</math> meters and an area of <math>168</math> square meters. In meters, what is the perimeter of the parkin…')
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem 14

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?

$\textbf{(A)}\ 52 \qquad\textbf{(B)}\ 58 \qquad\textbf{(C)}\ 62 \qquad\textbf{(D)}\ 68 \qquad\textbf{(E)}\ 70$

Solution

Let the sides of the rectangular parking lot be $a$ and $b$. Then $a^2 + b^2 = 625$ and $ab = 168$. Add the two equations together, then factor. \begin{align*} a^2 + 2ab + b^2 &= 625 + 168 \times 2\\ (a + b)^2 &= 961\\ a + b &= 31 \end{align*} The perimeter of a rectangle is $2 (a + b) = 2 (31) = \boxed{\textbf{(C)} 62}$

Invalid username
Login to AoPS