Question

the perimeter of isosceles triangle is 100cm. if each of its equale sides is 26cm,find the area of triangle​

Answer 1

Required Answer:

Given:

• Perimeter of isosceles triangle = 100 cm

• Measure of two equal sides = 26 cm

To calculate:

• Area of the triangle.

Calculation:

In order to calculate the area of the triangle, we need to calculate the third side first.

Measure of third side :

Let the third side be x cm.

We know that,

• Perimeter of triangle = Sum of all sides

→ 100 cm = ( 26 + 26 + x ) cm

→ 100 cm = ( 52 + x )cm

→ x cm = ( 100 - 52 ) cm

→ x cm = 48 cm

Therefore, measure of third side is 48 cm.

Now, we have :

• First side (a) = 26 cm

• Second side (b) = 26 cm

• Third side (c) = 48 cm

Calculating area :

By using heron's formula :

$\bold { Area \: of \: \triangle = \sqrt{s(s-a)(s-b)(s-c)} }$

Where,

• s = semi-perimeter

• s = semi-perimeter• a, b, c = sides of ∆

→ Semi-perimeter = $\sf {\dfrac{a + b+ c}{2}}$

→ Semi-perimeter = $\sf {\dfrac{100}{2}}$

→ Semi-perimeter = 50 cm

Now, substituting values in the formula :

→ Area = √50(50-26)(50-26)(50-48) cm²

→ Area = √50 × 24 × 24 × 2 cm²

→ Area = √57600 cm²

→ Area = 240 cm²

Therefore, area of the triangle is 240 cm².