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 $12cm$
• B. $6cm,3cm$ and $8cm$
• C. $7cm,6cm$ and $15cm$
• D. $7cm,7cm$ and $10cm$

Answer 1

The correct option is D $7cm,7cm$ and $10cm$

Let the length of the base of an isosceles triangle be $x$ cm.

Therefore, as per the given conditions,

Length of the congruent sides $=2x-13$ cm

Given, the perimeter of an isosceles triangle $=24$ cm.

Therefore, $x+2x-13+2x-13=24$

$\Rightarrow 5x-26=24$

$\Rightarrow 5x=24+26$

$\therefore x=10$

Base of a triangle $=10$ cm

Congruent sides $=2x-13$

$=2\times 10-13$$=20-13=7$ cm

Therefore, the length of sides are $7cm,7cm$ and $10cm$.