Question

1. 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

Answer:

7 cm, 10 cm, 7 cm

Step-by-step explanation:

Let the length of the nom congruent side be x.

Hence, length of each congruent side = 2x - 13

Perimeter of a triangle = Sum of lengths of all sides.

As given,

x + ( 2x - 13 ) + ( 2x - 13 ) = 24

5x - 26 = 24

5x = 50

x = 10 cm

Thus, 2x - 13 = 2 × 10 - 13 = 20 - 13 = 7 cm.

ANS = 7 cm, 10 cm, 7 cm

Answer 2

Let the length of the base be x and the congruent side of triangle be y respectively.

Perimeter of triangle :- x + y + y = 24

Therefore, x + 2y = 24 --(1)

According to the given condition we get,

y = 2x - 13

13 = 2x - y --(2) [ Multipy it with 2 ]

26 = 4x - 2y

4x - 2y = 26 --(3)

Adding equation (1) & (3) We get,

5x = 50

x = 50/5

x = 10

Therefore, the base of an given isosceles triangle is 10 cm.

Substituting the value of x = 10 in equation (1)

x + 2y = 24

10 + 2y = 24

2y = 24 - 10

2y = 14

y = 14/ 2

y = 7

Therefore, the congruent side of the given triangle if 7 & 7 cm respectively.