Question

The ratio of the side lengths of a quadrilateral is 2:7 8:12, and the perimeter is 522cm. what is the measure of the shortest side? Please help

Answer 1

Given ratios of the side lengths of a quadrilateral.

$2\colon7\colon8\colon12$

Let x be the factor of the given ratios.

$2x,\text{ 7x, 8x, 12x}$

The perimeter of the quadrilateral is calculated by the given formula.

$\text{Perimeter = sum of all the sides of the quadrilateral}$

Now, the perimeter of the quadrilateral is

$\begin{gathered} 2x+7x+8x+12x=522\text{ cm} \\ 29x\text{ = 522 cm} \\ x=\frac{522}{29}\text{ c}m \\ x=18\text{ cm} \end{gathered}$

Thus, the sides will be

$\begin{gathered} 2x\colon7x\colon8x\colon12x \\ =(2\times18)\colon(7\times18)\colon(8\times18)\colon(12\times18) \\ =36\colon126\colon144\colon216 \end{gathered}$

Thus, the shortest side will be 36.

Therefore, the given options c is correct.