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Question

The sides of a right triangle are a,a+d and a+2d, with a and d both positive. The ratio of a to d is:

A
1:3
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B
1:4
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C
2:1
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D
3:1
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E
3:4
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Solution

The correct option is C 3:1
Given:Sides of right angled triangle is a;a+d;a+2d[a,d>0]
To find:ad
Solution:Let AB=a;BC=a+d;CA=a+2d
ABC is right angled at B
InABC
AB2+BC2=AC2(pythagoras thm)
a2+(a+d)2=(a+2d)2
a2=(a+2d)2(a+d)2
a2=(a+2d+a+d)(a+2dad)[a2b2=(a+b)(ab)]
a2=2ad+3d2
a22ad=3d2
Adding d2to both the sides
a22ad+d2=4d2
(ad)2=4d2[(ab)2=a22ab+b2]
Taking squar-root on both the sides
ad=2d;ad=2d
a=2d;a=d
a=d is not possible as a&d are positive.
a=3d
ad=3

1011800_923035_ans_031919c92a3f4ef4a8711011d9517dff.png

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