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

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ΦLet 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

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


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