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.
