Question

a right angle triangle has the perimeter of 96cm. the length of its sides are in the ratio of 6:8:10. work out the area of the triangle

Answer 1

Answer:

384 centimeters squared.

Step-by-step explanation:

96/(6+8+10)

96/24 = 4

6×4 : 8×4 : 10×4

24:32:40

The length of its sides are in the ratio of 24:32:40

The longest side is the hypotenuse which is 40.

The area is base × height × 1/2 of a triangle.

32 × 24 × 1/2

768 × 1/2

=384

The area of the triangle is 384 cm squared.

Answer 2

Answer:

Area = 384 cm²

Step-by-step explanation:

Perimeter = 96 cm

Ratio = 6:8:10

So,

6x+8x+10x = 96

=> 24x = 96

Dividing both sides by 24

=> x = 4

So, The sides are

=> 24 cm

=> 32 cm

=> 40 cm

Now the area using Heron's Formula

Area = $\sqrt{s(s-a)(s-b)(s-c)}$

Where s is the semi-perimeter = 48 cm, a , b and c are the sides

Area = $\sqrt{48(48-24)(48-32)(48-40)}$

Area = $\sqrt{48(24)(16)(8)}$

Area = $\sqrt{147,456}$

Area = 384 cm²