Question

The sides of a triangle are in the ratio 3:5:7 and perimeter is 300 m. Find its area .

Answer 1

HOPE THAT IT HELPS YOU ............

Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Perimeter = 300m

Ratio = 3 : 5 : 7

Assume,

Sides

a = 3p

b = 5p

c = 7p

Perimeter of ∆ = a + b + c

300 = 3p + 5p + 7p

15p = 300

p = 300/15

p = 20

So the Sides,

a = 3p = 3 × 20 = 60 m

b = 5p = 5 × 20 = 100m

c = 7p = 7 × 20 = 140m

Semi Perimeter,

s = (a + b + c)/2

s = (60 + 100 + 140)/2

s = 300/2

s = 150 m

Now,

Using Heron’s formula :-

A = √s(s - a)(s - b)(s - c)

A = √150(150 - 60)(150 - 100)(150 - 140)

A = √150 × (90) × (50) × (10)

A = √(10 × 15) (9 × 10) × (5 × 10) × 10

A = √(10 × 10 × 10 × 10) × (5 × 3) × (9) × 5

A = √(10 × 10 × 10 × 10) × (5 × 5) × (3 × 3) × 3

A = 10 × 10 × 5 × 3 √3

A = 1500√3 m²

Therefore,

Area of the triangle = 1500√3 m²