Question

The base of an isosceles triangle is 3 cm longer than each of the other sides. If the perimeter is 54 cm, find the lengths of the sides.

Answer 1

Question:-

The base of an isosceles triangle is 3 cm longer than each of the other sides. If the perimeter is 54 cm, find the lengths of the sides.

Answer:-

Hint

Let length of equal sides be 'x' cm each.

Base = x + 3 cm

Perimeter = 54 cm

x + x + x + 3 = 54

3x + 3 = 54

3x = 51

x = 51/3

x = 17 cm

So the sides are 17 cm, 17 cm and 20 cm, respectively.

Answer 2

$\large\mathfrak \pink{Solution:-}$

$\underline \mathbb{GIVEN:-}$

The base of an isosceles triangle is 3 cm longer than each of the other sides.

Perimeter is 54 cm.

$\underline \mathbb{TO  \: FIND:-}$

Length of all the sides.

$\underline \mathbb{ASSUMPTION:-}$

In an Isosceles triangle 2 sides are equal.

Let, the 1st equal side be x

and the 2nd equal be x

and the 3rd side(base) be x + 3

$\underline \mathbb{BY  \: THE  \: PROBLEM:-}$

x + x + x + 3 = 54

or, 3x + 3 = 54

or, 3x = 54 - 3

or, 3x = 51

or, $x=\cancel\frac{51}{3}$

or, x = 17

$\underline \mathbb{ANSWER:-}$

Length of the 1st side = x = 17 cm

Length of the 2nd side = x = 17 cm

Length of the 3rd side = x + 3 = 17 + 3 = 20 cm