The perimeter of a triangular ground is 900m and its sides are in the ratio 3:5:4. Find the area of the ground.
Answers
Answered by
6
sides ratio = 3:5:4
so let the sides be 3x 5x. 4x
3x +. 5x + 4x= 900
12x = 900
x= 900/12
3x=900/12×3=225
4x=900/12×4=300
5x =900/12×5=375
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Answered by
5
Step-by-step explanation:
let the sides of triangle be 3x,5x,4x
3x+5x+4x=900
12x=900
x=75
3x=3×75=225
5x=5×75=375
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.
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