Question

The side of a triangle are in the ratio 3:5:7and it perimeter is 150 cm, then its area in cm√is.

Answer 1

Answer:

Let the common ratio be x

The three sides are - 3x, 5x and 7x

perimeter = 150 cm

=> 3x + 5x + 7x = 150

=> 15x = 150

=> x = 10

The three sides are- 30cm, 50cm, and 70cm

a = 30, b = 50 , c = 70 and s = (30+50+70)/3 = 50

$area = \sqrt{s \times (s - a) \times (s - b) \times (s - c)} \\ = \sqrt{75 \times (75 - 30) \times (75 - 50) \times (75 - 70)} \\ = \sqrt{75 \times 45 \times 25 \times 5 } = \sqrt{421875} = 649.51 {cm}^{2}$

Answer 2

let the coefficient of the ratio's be 'x'

perimeter=150

= 3x+5x+7x=150

15x=150

x=10

sides are : 30 , 50 , 70

S= 150/2

=75

Using heron's formula ;

area = √s(s-a) (s-b) (s-c)

=√75(75-30) (75-50) (75-70)

= √75(45) (25) (5)

=√5 ×5×3×5×3×3×5×5×5

= 5×5×5×3×√3

= 575√3 cm