Question

The length of a regulation soccer field is 110 meters. The diagonal length of the same soccer field is about 133.14 meters. About how wide is the regulation soccer field?

A. 23.14 meters
B. 243.14 meters
C. 172.7 meters
D. 75 meters​

Answer 1

Using the Pythagorean theorem, the width of the soccer field is calculated to be approximately 75 meters, which is answer choice D.

Step-by-step explanation:

To find the width of the regulation soccer field, we can use the Pythagorean theorem (a² + b² = c²), where 'a' represents the length of the soccer field, 'b' is the width we want to find, and 'c' is the diagonal length of the soccer field. We know that the length of the field ('a') is 110 meters and the diagonal ('c') is approximately 133.14 meters. Plugging these values into the theorem:

a² + b² = c² becomes 110² + b² = 133.14²

By solving for 'b', we get:

b² = 133.14² - 110²
b² = 17728.0996 - 12100
b² = 5628.0996
b = √5628.0996
b ≈ 75 meters

Therefore, the width of the soccer field is approximately 75 meters, which corresponds to answer choice D.

Answer 2

D

Step-by-step explanation:

Imagine this as a right angle triangle, where the diagonal length is the hypotenuse, the length is one side, and the width is the other.

We can therefore use Pythagoras' Theorem (or Pythagorean Theorem) to solve. The formula for this is a²+b²=c², where c is the hypotenuse, and a and b are the sides.

We can input the values we know to this formula to get the width. This gives 110²+b²=133.14² or 12100+b²=17 726.2596.

From there subtracting 12100 from both sides gives b²=5626.2596.

Square rooting b isolates it, leaving b=75.0083969.

Since the value of the diagonal was approximate, this can be assumed the b is 75m.

**This content involves Pythagoras' Theorem/Pythagorean Theorem, which you may wish to revise. I'm always happy to help!