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:

a) Approximate height of the statue: 144 feet

b) The approximate height is 1.7% greater that the actual height of the statue.

Explanation

1) Assume that the measures of the statue are proportional to the dimensions of the student. That means:

        statue's height                                   student's height

________________________   =    ______________________

length of the​ statue's right arm          length of student's right arm

⇒ x / 54 feet = (5 + 1/3) feet / 2 feet

⇒ x = 54 × (16/3) / 2 feet = (54×16) / (3×2) feet = 144 feet

Answer: 144 feet

2) Compare the approximate heigth obtained with the actual height:

144 feet - (143 feet + 9 inches) = 144 feet - (143 feet + 9/12 feet) = 1 feet - 9/12 feet

1 feet - 9/12 feet = 1 feet - 3/4 feet = 1/4 feet.

Hence, the approximate feet obtained is 1/4 feet larger than the actual height.

In relative terms that is : (1/4) / (143 + 3/4) = 0.0017 = 1.7%.