JEE Main 20204 SeptemberMorning Shift

Exam: JEE Main
Year: 2020
Date: 4 September
Shift: Morning Shift
Subject: Mathematics
Chapter: Heights and Distances

JEE Main 2020 · 4 September · Morning Shift · Mathematics · Heights and Distances

Two vertical poles AB = 15m and CD = 10m are standing apart on a...

Two vertical poles

AB = 15m

and

CD = 10m

are standing apart on a horizontal ground with points $A$ and

C

on the ground. If

P

is the point of intersection of

BC

and

AD,

then the height of

P

(in

m

) above the line

AC

is :

Two vertical poles AB = 15m and CD = 10m are standing apart on a horizontal ground with points A and C on the ground.

Options

A $20 / 3$
B $5$
C $10 / 3$
D $6$

Correct answer

D. $6$

Step-by-step solution

Two vertical poles AB = 15m and CD = 10m are standing apart on a horizontal ground with points A and C on the ground.

$\delta AQP ~ \delta ACD$

$⇒$ $\dfrac{x}{h} = \dfrac{x + y}{10} . . . \left(1\right)$

$∵$ $\delta CQP ~ \delta CAB$

$⇒ \dfrac{y}{h} = \dfrac{x + y}{15} . . . . \left(2\right)$

Adding \left(1\right) \text{ and } \left(2\right) $, we get</p><p>$ \dfrac{x + y}{h} = \left(x + y\right)\left(\dfrac{1}{10} + \dfrac{1}{15}\right) $</p><p>$ ⇒ h = 6.

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