Question

A girl of height 90 cm is walking away from the base of a lamp post at a speed of 120 cm/sec. If the lamp post is 360 cm above the ground, then the length of her shadow after 4 seconds is:

• A. 90 cm
• B. 120 cm
• C. 160 cm
• D. 180 cm

Hint:

When solving problems involving similar triangles, use proportionality to relate corresponding sides and solve for unknowns.

Answer 1

The Correct Option is C

Let the length of the shadow after 4 seconds be \(x\). Using similar triangles, the ratio of the height of the girl to the height of the lamp post is equal to the ratio of the length of the shadow to the sum of the girl's distance from the lamp post and the length of her shadow. Thus: \[ \frac{90}{360} = \frac{x}{120 + x} \] Cross-multiplying: \[ 90 \times (120 + x) = 360 \times x \] Expanding and solving: \[ 10800 + 90x = 360x \] \[ 10800 = 270x \quad \Rightarrow \quad x = \frac{10800}{270} = 40 \] Thus, the total length of the shadow after 4 seconds is \(120 + 40 = 160\) cm. Thus, the correct answer is option (3).