Question

The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is ______.

पर्याय

• 1322 cm² 

• 1311 cm² 

• 1344 cm² 

• 1392 cm² 

Answer 1

The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is 1344 cm².

Explanation:

The sides of a triangle area = 56 cm, b = 60 cm and c = 52 cm.

So, semi-perimeter of a triangle will be:

`s = (a + b + c)/2`

= `(56 + 60 + 52)/2`

= `168/2`

= 84 cm

Area of the triangle = `sqrt(s(s - a)(s- b)(s - c))`  ...[By heron’s formula]

= `sqrt(84(84 - 56)(84 - 60)(84 - 52))`

= `sqrt(84 xx 28 xx 24 xx 32)`

= `sqrt(4 xx 7 xx 3 xx 4 xx 7 xx 4 xx 2 xx 3 xx 4 xx 4 xx 2)`

= `sqrt(4^6 xx 7^2 xx 3^2)`

= 4³ × 7 × 3

= 1344 cm²