Question

The sides of a triangle are in the ratio 5 : 12 : 13. If its perimeter is 90 cm, find the area of the triangle.

Answer 1

Given:

• The sides of the triangle are in the ratio 5 : 12 : 13.
• The perimeter of the triangle is 90 cm.

Step wise calculation:

1. Let the sides of the triangle be 5x, 12x and 13x.

2. The perimeter is the sum of all sides:

5x + 12x + 13x = 90

30x = 90

x = `90/30` = 3

3. So, the sides of the triangle are:

5 × 3 = 15 cm

12 × 3 = 36 cm

13 × 3 = 39 cm

4. Since the ratio 5 : 12 : 13 is a Pythagorean triplet, this is a right triangle with the hypotenuse 39 cm.

5. The area of a right triangle is given by:

Area = `1/2` base × height

Here, base = 15 cm, height = 36 cm.

6. Calculate the area:

Area = `1/2 xx 15 xx 36`

= `1/2 xx 540`

= 270 cm²

The area of the triangle is 270 cm².