Latest SSC Aptitude Question SOLUTION: The perimeter of a right angled triangle is 4 times the shorter side. Find the ratio of other sides ??

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(#M40155644) SSC Numerical Ability question area and perimeter Keep an EYE

The perimeter of a right angled triangle is 4 times the shorter side. Find the ratio of other sides ??

Asked In SSC DEBARSHI DALAI (8 years ago)

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Devendra Marghade  (8 years ago)

4/5

If sides of a right angles triangle are x, y & z with shorter side=x and longer side(hypotenuse)=z, then perimeter=x+y+z=4x or x=(y+z)/3 ---(i)
Also y^2 + x^2= z^2 or z^2 - y^2= x^2 ---(ii)
From (i), x^2=(y^2+2yz+z^2)/9, substituting this value in (ii), z^2 -y^2=(y^2 +2yz +z^2)/9 or
10y^2 +2yz - 8z^2 =0
Dividing above equation by z^2, we get 10(y/z)^2 +2(y/z) -8 =0
By substituting y/z =a , 10a^2 +2a -8 =0 , 10a^2 +10a -8a -8 =0 ,(10a-8)(a+1)=0, so a=8/10=4/5
So ratio of other sides=y/z=a=4/5

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