Question

A student would like to find the height of a statue. The length of the​ statue's right arm is 54 feet. The​ student's right arm is 2 feet long and her height is 5 and one third feet. Use this information to find the height of the statue. How close is the approximate height to the​ statue's actual height of 143 ​feet, 9 inches from heel to top of​ head?

Answer 1

Answer:

The approximate height is 0.251 inches close to the​ statue's actual height of 143 ​feet, 9 inches from heel to top of​ head .

Step-by-step explanation:

Given :

The length of the​ statue's right arm is 54 feet.

The​ student's right arm is 2 feet long and her height is 5 and one third feet.

To Find : How close is the approximate height to the​ statue's actual height of 143 ​feet, 9 inches from heel to top of​ head?

Solution:

Let the height of the statue be x

The length of the​ statue's right arm is 54 feet.

The​ student's right arm is 2 feet long

Ratio of their arms length = 54:2

Height of girl = $5\frac{1}{3} =\frac{16}{3}$

Ratio of their heights = $x: \frac{16}{3}$

So, $\frac{x}{\frac{16}{3}}=\frac{54}{2}$

$x=\frac{16}{3} \times \frac{54}{2}$

$x=8 \times 18$

$x=144$

So, the approximate height is 144 feet.

Actual height of statue is 143 ​feet, 9 inches = $143 + 9 \times 0.0833333=143.749$

So, the difference between approximate height and actual height:

= 144-143.749

=0.251

Hence the approximate height is 0.251 inches close to the​ statue's actual height of 143 ​feet, 9 inches from heel to top of​ head .

Answer 2

Assuming that the dimensions are proportional, we have the following relationship:

$\frac{x}{5+\frac{1}{3}} = \frac{54}{2}$

Where,

x: approximate height of the statue

Clearing the value of x we have:

$x=\frac{54}{2}(5+\frac{1}{3})$

$x = 144$

On the other hand, we know that:

$1feet = 12inches$

Then, in relative terms, the relationship between the heights of the statue is:

$\frac{144-(143+\frac{9}{12}}{143+\frac{9}{12}}(100)$

$1.7$%

Answer:

The approximate height of the statue is:

$x = 144$

The difference with respect to the actual height is 1.7%.