Question

The sides of a triangle are in the ratio 25 : 17 : 12 and its perimeter is 540 cm. Its area is ______.

पर्याय

• 3600 cm²

• 4500 cm²

• 7200 cm²

• 9000 cm²

Answer 1

The sides of a triangle are in the ratio 25 : 17 : 12 and its perimeter is 540 cm. Its area is 9000 cm².

Explanation:

Let the sides be 25x, 17x and 12x.

Then 25x + 17x + 12x = 54x = 540.

⇒ x = 10, so the sides are 250, 170 and 120 cm.

Semi-perimeter s = `540/2` = 270.

Using Heron’s formula:

Area = `sqrt(s(s−a)(s−b)(s−c))` 

= `sqrt(270 xx (270 - 250) xx (270 - 170) xx (270 - 120))` 

= `sqrt(270 xx 20 xx 100 xx 150)` 

= `sqrt(81,000,000)`

= 9000 cm²