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?

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Answer 1 · 2016-10-25T13:43:18

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

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

$94.6 = (2 \cdot ((4 \cdot W) + 7.8) + (2 \cdot W)$ $94.6 = (2 * ((4 * W) + 7.8) + (2 * W)$

Simplifying and solving for $W$ $W$

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

$94.6 = (10 \cdot W) + 15.6$ $94.6 = (10 * W) + 15.6$

$79 = 10 \cdot W$ $79 = 10 * W$

$W = 7.9$ $W = 7.9$

and

$L = (4 \cdot W) + 7.8$ $L = (4 * W) + 7.8$

$L = (4 \cdot 7.9) + 7.8$ $L = (4 * 7.9) + 7.8$

$L = 31.6 + 7.8 = 39.4$ $L = 31.6 + 7.8 = 39.4$