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SSC CPO 2019 PYQ — Question 101

SSC CPO Tier I - 11th December 2019 - Shift 1 • Quantitative Aptitude • Q101

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In ΔABC, ∠C = 90º and CD is perpendicular to AB at D. If AD/BD = √k, then AC/BC = ?

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Correct answer: D

Explanation

  The correct answer is option 4 i.e. 4√k

Understanding

Given:

AD/BD = √k

Use of similarity of triangles:

If 2 triangles are similar then the sides of 2 triangles will be proportional.

Application

 

In triangles BCA and BDC:

∠BCA = ∠BDC

∠B is common.

So, triangles BCA and BDC are similar.

So,

BA/BC = BC/BD

BC2 = BA × BD …………. (1)

Now in triangles ACB and ADC:

∠ACB = ∠ADC

∠A is common.

So, triangles ACB and ADC are similar.

So,

AB/AC = AC/AD

AC2 = AB × AD …………. (2)

From both the equations:

AC2/BC2 = (AB × AD)/(BA × BD) = AD/BD

AC2/BC2 = √k

So,

AC/BC = 4√k