Question

A 5.ft tall man casts a shadow along the ground that is 8 ft. long. At the same time a giraffe casts a shadow that is 12 ft. long. How tall is the Giraffe?

Answer 1

Answer : 7.5 ft

Explanation:

when the length of the shadow is 8ft, the actual height of the man = 5ft

8:5

let the giraffe be 'x' ft tall.

if the length of the shadow is 12ft, actual height = x ft

12:x

8:5 x 12:x

`(8)/(5)` ×
`(12)/(x)`

x=
`(15)/(2)`

x=7.5 ft

Therefore, the giraffe is 7.5ft tall.

Answer 2

`7.5\; {\rm ft}`.

Explanation:

The height of objects nearby under the sun are approximately proportional to the length of their shadows.

In other words, if the man and the giraffe are near each other and under the sun:

`\begin{aligned} \frac{\text{height of man}}{\text{length of shadow of man}} = \frac{\text{height of giraffe}}{\text{length of shadow of giraffe}}\end{aligned}`.

Given that:

• 
  `(\text{height of man}) = 5\;{\rm ft}`,
• 
  `(\text{length of shadow of man}) = 8\;{\rm ft}`, and
• 
  `(\text{length of shadow of giraffe}) = 12\; {\rm ft}`.

Rearrange the equation to find
`(\text{height of giraffe})`:

`\begin{aligned} (\text{height of giraffe}) &= (\text{length of shadow of giraffe})* \frac{\text{height of man}}{\text{length of shadow of man}} \\ &= 12\; {\rm ft} * \frac{5\; {\rm ft}}{8\; {\rm ft}} \\ &= 7.5\; {\rm ft}\end{aligned}`.