01 · RATIO SIDE PROBLEMS
Sides Given in Ratio
SOLVED EXAMPLE
Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area.
1. Let the sides be 12x, 17x, and 25x:
Perimeter = 12x + 17x + 25x = 540
54x = 540 ⟹ x = 10
Sides: a = 120 cm, b = 170 cm, c = 250 cm
54x = 540 ⟹ x = 10
Sides: a = 120 cm, b = 170 cm, c = 250 cm
2. Semi-perimeter s = 540 / 2 = 270 cm:
Area = √[ 270 × (270 - 120) × (270 - 170) × (270 - 250) ]
= √[ 270 × 150 × 100 × 20 ]
= √[ 81,000,000 ] = 9000 cm²
= √[ 270 × 150 × 100 × 20 ]
= √[ 81,000,000 ] = 9000 cm²