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

Option C: 9 feet is the correct answer

Step-by-step 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

`(10)/(18)=(5)/(x)`

`10x=90`

`x=9`

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

Answer 2

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 = (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 = (5)/(s)`

Compare the value of k .

`(10)/(18) = (5)/(s)`

`s = (18* 5)/(10)`

s = 9 ft

Therefore the shadow of the woman be 9 ft .

Option (C) is correct .