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JEE Main 20198 AprilEvening Shift

Exam: JEE Main
Year: 2019
Date: 8 April
Shift: Evening Shift
Subject: Mathematics
Chapter: Heights and Distances

JEE Main 2019 · 8 April · Evening Shift · Mathematics · Heights and Distances

Two vertical poles of height, 20m and 80m stand apart on a...

Two vertical poles of height,

20m

and

80m

stand apart on a horizontal plane. The height (in meters) of the point of intersection of the lines joining the top of each pole to the foot of the other, from this horizontal plane is: Two vertical poles of height, 20m and 80m stand apart on a horizontal plane. The height (in meters) of the point of

Two vertical poles of height, 20m and 80m stand apart on a horizontal plane. The height (in meters) of the point of

Options

A $16$
B $12$
C $18$
D $15$

Correct answer

A. $16$

Step-by-step solution

Two vertical poles of height, 20m and 80m stand apart on a horizontal plane. The height (in meters) of the point of

Equation of line $OQ$ $y = \dfrac{80}{a}x$

Equation of line $AB$ $\dfrac{x}{a} + \dfrac{y}{20} = 1$

Solving for $P\left({x}_{0}, {y}_{0}\right), \dfrac{a{y}_{0} / 80}{a} + \dfrac{{y}_{0}}{20} = 1$

$⇒ {y}_{0}\left(\dfrac{1}{80} + \dfrac{1}{20}\right) = 1 ⇒ {y}_{0} = 16$

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