Question

20. Sides of a triangle are in the ratio 12: 17 :25 and its perimeter is 540 cm. Find its area.​

Answer 1

A= 9000 cm²

Explanation:

First of all, we need all sides to find the area so for that we need the total sum of ratios.

The sum of ratios= 12+17+25= 54

So to find a side we need to divide the ratio by the sum of ratios and then multiply it with the perimeter.

side a=
`(12)/(54)`×540 = 120 cm

side b=
`(17)/(54)`×540 = 170 cm

side c=
`(25)/(54)`×540= 250 cm

We got all the sides and to find the area we need to use the Heron formula:

A=
`(1)/(4)`×√(4a²b² - (a²+b²-c²)²)

A=
`(1)/(4)`×√(4×120²×170² - (120²+170²-250²)²)

Solving the equation you get:

A= 9000 cm²

​