# The length of a rectangle is 7.8 cm more than 4 times the width. If the perimeter of the rectangle is 94.6 cm, what are its dimensions?

Oct 25, 2016

Width of the rectangle is 7.9 cm and the Length is 39.4 cm.

#### Explanation:

We know the equation for Perimeter is $P = \left(2 \cdot L\right) + \left(2 \cdot W\right)$ we can therefore substitute the following:

94.6 = (2 * ((4 * W) + 7.8) + (2 * W)

Simplifying and solving for $W$

$94.6 = \left(8 \cdot W\right) + 15.6 + \left(2 \cdot W\right)$

$94.6 = \left(10 \cdot W\right) + 15.6$

$79 = 10 \cdot W$

$W = 7.9$

and

$L = \left(4 \cdot W\right) + 7.8$

$L = \left(4 \cdot 7.9\right) + 7.8$

$L = 31.6 + 7.8 = 39.4$