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Question
The perimeter of a triangle ABC is 37 cm and the ratio between the lengths of its altitudes be 6: 5: 4. Find the lengths of its sides.
Let the sides be x cm, y cm, and (37 - x - y) cm. Also, let the lengths of altitudes be 6a cm, 5a cm, and 4a cm.
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Solution
Consider that the sides be x cm, y cm, and (37 - x - y) cm. also, consider that the lengths of altitudes be 6a cm, 5a cm, and 4a cm.
∴ Area of a triangle = `1/2` x base x altitude
∴ `1/2 xx x xx 6a = 1/2 xx y xx 5a = 1/2 xx ( 37 - x - y) xx 4a`
6x = 5y = 148 - 4x - 4y
6x = 5y and 6x = 148 - 4x - 4y
6x - 5y = 0 and 10x + 4y = 148
Solving both the equations, we have
X = 10 cm, y = 12 cm and ( 37 - x - y ) cm = 15cm.
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