Question

Solve the following problems using two variables.
(ii) 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

Let the length of one congruent side of the isosceles triangle be x cm and the length of the base be y cm.
According to the question, we have:
2x + y = 24 ...(1)
and
x = 2y $-$ 13
⇒ x$-$2y = $-$13 ...(2)
Multiplying eq. (1) by 2, we get:
4x + 2y = 48 ...(3)
Adding (2) and (3), we get:
x $-$ 2y = $-$13
4x + 2y = 48
--------------------------
5x = 35
⇒ x = 7
Substituting the value of x in (1), we get:
2(7) + y = 24
⇒ 14 + y = 24
⇒ y = 10
i.e., congruent side = 7 cm and base = 10 cm
∴ The sides of the triangle are 7 cm, 7 cm and 10 cm.