Question

Two vertical poles of heights, 20 m and 80 m 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 ______.

Options

• 15

• 18

• 12

• 16

Answer 1

Two vertical poles of heights, 20 m and 80 m 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 16.

Explanation:

Equations of lines OB and AC are respectively

y = `80/x_1x`  ...(i)

`x/x_1 + y/20` = 1  ...(ii)

∵ Equations (i) and (ii) intersect each other

∴ Substitute the value of x from equation (i) equation (ii), we get

`y/80 + y/20` = 1

⇒ y + 4y = 80 ⇒ y = 16 m

Hence, height of intersection point is 16 m.