Question

2. The sum of the perimeters of similar quadrilaterals is 22.5 dm. Find the perimeters of the quadrilaterals if the similarity coefficient k = 1.25.

Answer 1

Given:

The sum of the perimeters of similar quadrilaterals is 22.5 dm. The similarity coefficient k = 1.25.

Required:

To find the perimeters of the quadrilaterals.

Step-by-step explanation:

The quadrilaterals are similar and the similarity coefficient is k = 1.25.

If the quadrilateral is similar then the ratio of their corresponding sides is equal.

Let the perimeter of the one quadrilateral is x then the perimeter of the other quadrilateral will be 1.25x

Now

`\begin{gathered} x+1.25x=22.5 \\ x(1+1.25)=22.5 \\ 2.25x=22.5 \\ x=(22.5)/(2.25) \\ x=10 \end{gathered}`

Thus the perimeter of the one quadrilateral is 10dm.

The perimeter of the other quadrilateral = 1.25 x 10 = 12.5 dm

Final Answer:

Thus the perimeter of the quadrilaterals is 10dm and 12.5 dm.