Question

A quadrilateral has three congruent sides. Each of the congruent sides is 5 cm shorter than the forth side. If the quadrilateral has a perimeter of 33 cm, find the length of the longest side

Answer 1

The length of the three congruent sides is 7 cm and the fourth side length is 12cm.

Given quadrilateral has three congruent sides and perimeter of quadrilateral is 33 cm.

A quadrilateral can be expressed as ABCD and three congruent sides are AB, BC, CD and the fourth side is AD.

Let AD=x

then AB=BC=CD=x-5

This means if all the sides of a quadrilateral are known, we can get its perimeter by adding all its sides.

So, Perimeter = AB + BC + CD + DA.

Substitute values

(x-5)+(x-5)+(x-5)+x=33

4x-15=33

    4x= 48

     x=12

Hence the fourth side length is 12cm and the other sides are 7 cm longer.

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