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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.

Sagot :

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.

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

[tex]\begin{gathered} x+1.25x=22.5 \\ x(1+1.25)=22.5 \\ 2.25x=22.5 \\ x=\frac{22.5}{2.25} \\ x=10 \end{gathered}[/tex]

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.

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