Question

Two vertical poles AB = 15 m and CD = 10 m 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 ______.

Options

• `20/3`

• 5

• `10/3`

• 6

Answer 1

Two vertical poles AB = 15 m and CD = 10 m 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 6.

Explanation:

Let PE ⊥ AC, AE = m and EC = n

∵ ΔAEP ∼ ΔACD, `"m"/("PE") = ("m" + "n")/10`

`\implies "PE" = (10"m")/("m" + "n")`  ...(i)

∵ ΔCEP ∼ ΔCAB, `"n"/("PE") = ("m" + "n")/15`

`\implies "PE" = (15"n")/("m" + "n")`  ...(ii)

From (i) and (ii),

10m = 15n `\implies` m = `3/2"n"` So, PE = 6 ...[from (i)]