Question

Rohan is very intelligent in maths. He always try to relate the concept of maths in daily life. One day he is walking away from the base of a lamp post at a speed of 1 m/s. Lamp is 4.5 m above the ground.


If after 2 second, length of shadow is 1 meter, what is the height of Rohan ?
(3 Marks)

Answer 1

Given: Speed of Rohan = 1 m/s, Height of lamp = 4.5 m
Distance travelled by Rohan in 2 second
= (1 m/s)*(2 s) = 2 m
Hence, BD = 2 m.
DE = 1 m (Given) (0.5 Marks)
Consider △ABE and △CDE.
∠AEB = ∠CED (Common angle)
∠ABE = ∠CDE (Both are 90°)
∠BAE = ∠DCE (By angle sum property of triangle)
△ABE ~ △CDE (0.5 Marks)
$\frac{AB}{CD}$ = $\frac{BE}{ED}$
$\frac{4.5}{CD}$ = $\frac{3}{1}$
CD = 1.5 m (2 Marks)