Question

The perimeter of a right angled triangle is 96cm

The lengths of its sides are in the ratio 6:8:10

Work out the area of the triangle in cm^2​

Answer 1

384 cm^2

Explanation:

Let the lengths of the sides of the right-angled triangle be 6x, 8x, and 10x, where x is a constant.

Since the perimeter of the triangle is 96 cm, we have:

6x + 8x + 10x = 96

24x = 96

x = 4

Therefore, the lengths of the sides of the triangle are 24 cm, 32 cm, and 40 cm.

The area of a right-angled triangle is given by the formula:

Area = (1/2) * base * height

where the base and height are the two shorter sides of the triangle.

Using the Pythagorean theorem, we can determine that the base and height of the triangle are 24 cm and 32 cm, respectively.

Therefore, the area of the triangle is:

Area = (1/2) * base * height

Area = (1/2) * 24 cm * 32 cm

Area = 384 cm^2

Therefore, the area of the right-angled triangle is 384 cm^2.