Question

The perimeter of an isosceles triangle is 24cm. The length of its congruent sides is 13cm
less than twice the length of its base. Find the lengths of all sides of the triangle

Answer 1

Let ∆ABC be an isosceles triangle.

In which,

BC be a base and AB , AC be the two congruent sides of ∆ABC.

Let the length of base BC of an isosceles triangle be X cm.

Then the length of congruent sides AB and AC = (2X-13)

LENGTH of it's two congruent side is 2(2X -13) = 4X -26

AB + AC = 4X-26

Perimeter of triangle = 24

AB + AC + BC = 25

(4X -26+ X) = 24

5X = 24+26

5X = 50

X = 50/5

X = 10

Length of base of an isosceles triangle = X = 10 cm

And,

The Length of it's congruent sides = 2X -13 = 2 × 10 -13 = 20 - 13 = 7 cm

Answer 2

Answer:

Step-by-step explanation:

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.