# The perimeter of a rectangle is 54cm, the area of the same rectangle is 176cm squared, what is the dimensions of the rectangle?

Mar 27, 2018

11 by 16

#### Explanation:

Set up two equations

$2 x + 2 y = 54$

$x \times y = 176$

Solving the first equation for x

$2 x + 2 y - 2 y = 54 - 2 y$ this gives

$2 x = 54 - 2 y$ Divide both sides by 2

$\left(2 \frac{x}{2}\right) = \frac{54 - 2 y}{2}$ This gives.

$x = 27 - y$ putting this value into the second equation gives.

$\left(27 - y\right) \times y = 176$ multiplying across the parenthesis gives

$27 y - {y}^{2} = 176$ subtracting 176 from both sides gives
is
$27 y - {y}^{2} - 176 = 0$ multiplying by negative one gives

$- 27 y + {y}^{2} + 176 = 0$ factoring this into y gives

$\left(y - 11\right) \times \left(y - 16\right) = 0$ Solving for both y's gives

$y = 11 , y = 16$