Question

the perimeter of a triangle is 288 meter and the ratio of the sides is 3:4:5 find the area of the triangle

Answer 1

As perimeter is the sum of all sides of triangle here
So let the common multiple be x
So sides are 3x,4x,5x
ATQ
3x +4x+5x= 288
12 x =288
x = 288/12
x = 24
So the sides of triangle are 72, 96 and 120
Area =1/2 base × height
Here a, b are small sides. c hypotenuse)
So Area = 1/2×72×96 = 3456

Answer 2

Let the common multiple of side be x

1st side :- 3xm

2nd side :- 4xm

3rd side :- 5xm

Perimeter = 288m

( Perimeter of the figure is the sum of all side of the figure )

side 1 + side 2 + side 3 = 288

3x + 4x + 5x = 288

12x = 288

x = 288/12

x = 24

___________________________

1st side :- 3x = 3 × 24 = 72m

2nd side :- 4x = 96m

3rd side :- 5x = 120m


Since sides are forming right angle triangle as :-

( 120 )² = ( 72 )² + ( 96 )²

14400 = 14400

hence ,

area of ∆ = 1/2 × base × height

area of ∆ = 1/2 × 72 × 96

area of ∆ = 3456m²