Two vertical poles of height 10m and 40m stand apart on a...

Two vertical poles of height

10m

and

40m

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 10m and 40m stand apart on a horizontal plane. The height (in meters) of the point of

Two vertical poles of height 10m and 40m stand apart on a horizontal plane. The height (in meters) of the point of

Options

A $8$
B $10$
C $6$
D $4$

Correct answer

A. $8$

Step-by-step solution

Let

A\left(0,0\right), D\left(0,10\right),

B\left({x}_{1}, 0\right), C\left({x}_{1} ,40\right)

Equation of

AC ⇒ y = \dfrac{40}{{x}_{1}}x

… \left(1\right)

<br />Equation

BD ⇒ y - 10 = \dfrac{- 10}{{x}_{1}}x

&hellip; \left(2\right)

From \left(1\right)

and \left(2\right)

, we get,

\dfrac{{x}_{1} ⋅ y}{40} = \dfrac{- \left(y - 10\right) ⋅ {x}_{1}}{10}

y = - 4y + 40 ⇒ y = 8

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