Question

The sides(or leg) of right angled triangle are in the ratio 3:4.If its area is 1014 cm²,find its hypotenuse

Answer 1

the two sides of a triangle are 3x and 4x
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see the picture

Answer 2

let the common ratio be = X
therefore : 3x×4x×1/2 = 1014cm^2
=> 12x^2×1/2 = 1014
=> 12x^2 = 1014×2
=> 12x^2 = 2028
=> X^2 = 2028/12
=> X^2 = 169
=> X = √169
=> X = 13

Now,
3x = 3(13)
=> 39cm.

4x = 4(13)
=> 52cm.

H = hypotenuse

by Pythagoras theorem,
52^2+39^2 = H^2
2704+1521 = H^2
4225 = H^2
√4225 = H
65 = H

So, the length of the hypotenuse is 65 cm