Question

The sides of a right triangle are in the ratio 3:4 A rectangle is described on its hypotenuse ,the hypotenuse being the longer side of the rectangle is four fifth of it's length find the shortest side of the right triangle ,if the perimeter of the rectangle is 180 cm

Answer 1

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given : right triangle are in the ratio 3:4:A
let ratio coefficient = x
so,
sides = 3 x  and 4 x
we know that
hypotenuse^2  = adjacent^2 + opposite^2
hypotenuse^2  = (3x)^2 +(4x​)^2
hypotenuse^2  = 9x^2 + 16x^2
hypotenuse^2  = 25x^2
hypotenuse  = 5 x
as given :the hypotenuse being the longer side of the rectangle is four fifth of it's length
so,
length = 5x
and 
breath  =5x X 4/5 = 4x
we know perimeter of rectangle is 180cm
so,
2(5 x + 4 x) =180
2(9 x)  = 180
18 x  = 180   
x=180/18
x  = 10
so, 
side of triangle = 3(10) =30 cm , 4(10) = 40 cm ,
And  
hypotenuse = 5(10) = 50
shortest side of right angle  triangle  =  30

thanx

Answer 2

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