Question

The perimeter of a triangular ground is 900m and its sides are in ratio 3:5:4. Using heron's formal find the area of the ground

Answer 1

Heya !!!

Let sides of the triangle are 3X , 5X and 4X.

Perimeter of triangle = 900 m

Sum of all three sides = 900 m

3X + 5X + 4X = 900

12X = 900

X = (900/12) m

X = 75 m

Therefore,

3X = 3 × 75 = 225 m

5X = 5 × 75 = 375 m

And,

4X = 4 × 75 = 300

Sides of the triangle are 225 m , 375 m and 300 m.

Let,

A = 225 m

B = 375 m

And,

C = 300 m

Semi perimeter ( S ) = 1/2 × ( A + B + C )

=> 1/2 × ( 225 + 375 + 300 )

=> 1/2 × ( 900 )

=> 450 m

( S - A ) = 450 - 225 = 225 m

( S - B ) = 450 - 375 = 75 m

And,

( S - C ) = 450 - 300 = 150 m

Therefore,

Area of triangle = ✓S ( S - A ) ( S - B ) ( S - C )

=> ✓450 × 225 × 75 × 150

=> ✓1139062500

=> 33750 m².

★ HOPE IT WILL HELP YOU ★

Answer 2

perimeter = 900m ratio 3:5:4 then 3×900 2700. the answer is 2700. this is vedic maths. try it.