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Question

# The perimeter of an isosceles triangle is 24cm. The length of its congruent sides is 13cm less than twice the length of its base. Find the lengths of all sides of the triangle.

A
5cm,5cm and 12cm
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B
6cm,3cm and 8cm
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C
7cm,6cm and 15cm
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D
7cm,7cm and 10cm
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Solution

## The correct option is D 7cm,7cm and 10cmLet the length of the base of an isosceles triangle be x cm.Therefore, as per the given conditions,Length of the congruent sides =2x−13 cmGiven, the perimeter of an isosceles triangle =24 cm.Therefore, x+2x−13+2x−13=24⇒5x−26=24⇒5x=24+26∴x=10Base of a triangle =10 cmCongruent sides =2x−13=2×10−13=20−13=7 cmTherefore, the length of sides are 7 cm,7 cm and 10 cm.

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