Question

Perimeter of an isosceles triangle is 40cm and each of the equal sides is 15cm. Find the area of a triangle.​

Answer 1

Answer:

Step-by-step explanation:

Let the sides be of length x cm

Sum of two equal sides is x+x = 2x cm

Therefore base = 2x/3 cm

A/Q,

2x + 2x/3 = 40

(6x+2x) / 3 = 40

8x/3 = 40

8x = 40*3

x = 120/8

x = 15

so, the length of equal sides = 15 cm

& length of base = 2x/3 = 30/3 = 10 cm

Hope it will help you !!!

Answer 2

Given:

Equal sides = b = c = 15 cm.

Perimeter = a+b+c = 40 cm.

Finding the other side:

a+b+c = 40.

40 = a + 15 + 15.

40 = a + 30.

a = 40 - 30.

a = 10 cm.

Finding the area using heron's formula:

Area = √s(s-a)(s-b)(s-c) where s is the semi-perimeter of the triangle and a,b and c are the sides of the triangle.

S = perimeter/2 = 40/2 = 20 cm.

Area = √20(20-10)(20-15)(20-15)

Area = √20*10*5*5

Area = 5*10√2

Area = 50√2 cm²