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

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 .

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(1)/(3) =(16)/(3)`

Ratio of their heights =
`x: (16)/(3)`

So,
`(x)/((16)/(3))=(54)/(2)`

`x=(16)/(3) * (54)/(2)`

`x=8 * 18`

`x=144`

So, the approximate height is 144 feet.

Actual height of statue is 143 ​feet, 9 inches =
`143 + 9 * 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:

`(x)/(5+(1)/(3)) = (54)/(2)`

Where,

x: approximate height of the statue

Clearing the value of x we have:

`x=(54)/(2)(5+(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:

`(144-(143+(9)/(12))/(143+(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%.