2. 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.

Solution : Let the length of the base of the isosceles triangle be x cm and the length of congruent sides be y cm.

Then from the given conditions,

Perimeter of triangle = 24 cm.

∴ x + y + y = 24

∴ x + 2y = 24 ............. eq. no. (1)

According to second condition,

y = 2x – 13

∴ 2x – y = 13 ................. eq. no. (2)

Multiplying equation (2) by 2 we get

4x – 2y = 26 ................. eq. no. (3)

Adding equation (1) and (3)

x + 2y = 24

4x – 2y = 26

5x     =   50

∴ x = 50/5

∴ x = 10

Substituting x = 10 in eq. (1)

x + 2y = 24

∴ 10 + 2y = 24

∴ 2y = 24 – 10

∴ 2y = 14

∴ y = 14/2

∴ y = 7.

∴ The lengths of the sides of the triangle are 7 cm, 7 cm and 10  cm.