Question

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

Answer 1

Length of base of isosceles triangle = x cm

∴ Length of congruent side = 2x – 13 cm

Perimeter of isosceles triangle = 24 cm  ......[Given]

∴ Perimeter of isosceles triangle = Base + Congruent sides

∴ x + 2x – 13 + 2x – 13 = 24

∴ 5x – 26 = 24

∴ 5x = 26 + 24

∴ 5x = 50

∴ x = ${\displaystyle \frac{50}{5}}$

∴ x = 10

∴ Base = 10 cm

Length of congruent side = 2x – 13

= 2 × 10 – 13

= 20 – 13

= 7

∴ Base is 10 cm and each congruent side is 7 cm in length.