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Question
The ratio of the shorter sides of a right angled triangle is 5 : 12. If the perimeter of the triangle is 360 cm, find the length of the longest side.
Solution
Let the two shorter sides of a right-angled triangle be 5x and 12x.
Third (longest side)
= `sqrt((5x)^2 + (12x)^2)`
= `sqrt(25x^2 + 144x^2)`
= `sqrt(169x^2)`
= 13x
But 5x + 12x + 13x = 360cm
⇒ 30x = 360
⇒ x = `(360)/(30)` = 12
∴ Length of the longest side = 13x
= 13 x 12cm
= 156cm.
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