Question

the side of a triangle are in the ratio 5:7:8 and its perimeter is 300 cm .find its area
for class 9​

Answer 1

Given:

The side of a triangle are in the ratio 5:7:8 and its perimeter is 300 cm.

To find:

The area of the triangle

Solution:

The ratio of the sides of triangle is given by 5x, 7x and 8x

Perimeter is 5x+7x+8x = 20x

Perimeter = 300

20x = 300

x = 15

So the sides are:

• a=5x = 5.15 = 75 cm
• b=7x = 7.15 = 105 cm
• c=8x = 8.15 = 120 cm

Area of  the triangle can be find by the herons formula

semi perimeter = s = 150 cm

• $\sqrt{s(s-a)(s-b)(s-c)}$
• $\sqrt{150(150-75)(150-105)(150-120)}$
• $\sqrt{150.75.45.30}$
• $2250\sqrt{3}$
• 2250×1.732
• 3897 cm²

Answer 2

Answer:

Given:

The side of a triangle are in the ratio 5:7:8 and its perimeter is 300 cm.

To find:

The area of the triangle

Solution:

The ratio of the sides of triangle is given by 5x, 7x and 8x

Perimeter is 5x+7x+8x = 20x

Perimeter = 300

20x = 300

x = 15

So the sides are:

a=5x = 5.15 = 75 cm

b=7x = 7.15 = 105 cm

c=8x = 8.15 = 120 cm

Area of  the triangle can be find by the herons formula

semi perimeter = s = 150 cm