Question

the perimeter of a triangle are the ground is 900 M and its sides are in the ratio 3 ratio 5 ratio 4 ratio using herons formula 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

hey dear

here is your answer

___________________________________

perimeter of triangle = 900 M

and it's sides = 3 : 4: 5

Let the first side be = 3x

let second side be = 5x

let third side be = 4x

perimeter = ${ a+ b + c$

perimeter = 3x + 5x + 4x = 900

perimeter = 12x = 900 = 900 / 12 = 75

first side = 75 * 3 = 225m

second side = 75 * 5 = 375m

third side = 75 * 4 = 300m

so, semi perimeter = a + b + c / 2

= 900 / 2 = 450m

area of triangle

√S ( S - a) ( S - b) ( S - c)

√450 ( 450 - 225 ) * ( 450 - 375 ) * ( 450*300)

√450 * 225 * 75 * 150

√11390626500

= 33750 cm²

${ hence answer is 33750 cm² }$

hope it helps

thank you