Question

A 10 ft tall statue standing next to a woman casts an 18 ft shadow. If the woman is 5 ft tall, then how long is her shadow? A 3 ft B 6 ft C 9 ft D 32 ft

Answer 1

Answer

Find out the how long is woman shadow .

To prove

Let us assume that the height = x

Let us assume that the shadow = y

(As shadow increase with the increase in the height.)

$x\propto y$

x = ky

Where k is constant of proportionality.

As given

A 10 ft tall statue standing next to a woman casts an 18 ft shadow.

10 = k × 18

$k = \frac{10}{18}$

As given

If the woman is 5 ft tall .

Let us assume that the shadow of woman be s .

Put in the proprtionality equation .

5 = k × s

$k = \frac{5}{s}$

Compare the value of k .

$\frac{10}{18} = \frac{5}{s}$

$s = \frac{18\times 5}{10}$

s = 9 ft

Therefore the shadow of the woman be 9 ft .

Option (C) is correct .

     

Answer 2

Option C: 9 feet is the correct answer

Explanation:

Height of the statue = 10 feet

Height of the shadow = 18 feet

Woman's standing next to the statue height = 5 feet

Let us assume her shadow to be = x feet

Using the concept of proportionality

$\frac{10}{18}=\frac{5}{x}$

$10x=90$

$x=9$

Hence, the height of woman's shadow is 9 feet.