The ratio of the shorter side pf a right angled triangle is 5:12.If the perimeter of the triangle is 420cm,find the length of the longest side. please give step by step explanation.
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Hypotenuse is the longest side of right angled triangle.
Let the two other sides, which are in fact the shorter sides, be ‘5x’ cm & ‘12x’ cm
Let the hypotenuse be ‘h’cm
Applying Pythagoras theorem,
(5x)^2 + (12x)^2 = h^2
=> 125x^2 + 144x^2 = h^2
=> h^2 = 169x^2
=> h = 13x (Taking square root of both sides)
Since, perimeter = 420,
5x + 12x + 13x= 420
=> 30x=420
=>x = 14
Therefore, longest side = hypotenuse = h =13x=13 into 14=182 cm
Ans = 182 cm
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