Question

an isoscles triangle has perimeter 42 cm and each of equal sides is 15cm.find the area of the triangle

Answer 1

Answer:

Area of triangle is = 18 $\sqrt{21}$cm²

Step-by-step explanation:

Perimeter of isosceles triangle=42cm

Length of equal sides=15cm

Let third side of triangle=x cm

According to problem,

x+15+15=42

x= 42 - 30

x= 12

∴ Third side of triangle=12cm  

Using Heron's formula  

Area of triangle=  

sq. units  

where s = a + b + c / 2

s = 42 / 2

s = 21

Area of triangle = $\sqrt{21 (21 - 15) ( 21 - 15 ) (21 - 12)}$ cm²

= $\sqrt{21 (6) (6) (9)}$ cm²

=$\sqrt{ 7 * 3 * 3 * 2 * 2 * 3 * 3 * 3}$cm²

=$3 * 2 *3\sqrt {7 * 3}$cm²

= 18 cm²