Question

The heights of two vertical lamp posts are 33 m and 24 m high. If the distance between them is 40 m, then what will be the distance between their tops?

(a) 47.89m

(b) 56.56m

(c) 32.81m

(d) 41m

This question was posed to me during an online interview.

The question is from Pythagoras Theorem topic in portion Triangles of Mathematics – Class 10

Answer 1

Right option is (d) 41m

Easy explanation: Here, DC and AB are two lampposts of height 24 m and 33 m respectively.

The distance BC is 40m.

Now, draw a line perpendicular to AB from D.

Now, AED is a right-angled triangle, right angled at E.

AB = AE + EB

33 = AE + DC

33 = AE + 24

33 – 24 = AE

AE = 9m

In ∆AED,

AD^2 = DE^2 + EA^2

AD^2 = 40^2 + 9^2

AD^2 = 1600 + 81

AD^2 = 1681

AD = √1681 = 41 m

The distance between the two lampposts is 41 m.