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=(522)/(29)\text{ c}m \\ x=18\text{ cm} \end{gathered}`

Thus, the sides will be

`\begin{gathered} 2x\colon7x\colon8x\colon12x \\ =(2*18)\colon(7*18)\colon(8*18)\colon(12*18) \\ =36\colon126\colon144\colon216 \end{gathered}`

Thus, the shortest side will be 36.

Therefore, the given options c is correct.