Question

The dimensions of a gymnastic floor are 40 ft by 40 ft. The performance floor is 1 ft less, or 39 ft, per side. What is the length of the diagonal a gymnast must travel to get to the other side of the performance floor? Write your answer in radical form, if necessary. Enter your answer in the box.

PLEASE HELP!!!​

Answer 1

39√2 feet

Explanation:

You want the length of the diagonal of a square that is 39 feet on a side.

Diagonal

The Pythagorean theorem can be used to find the length of the diagonal. It tells you the length of the hypotenuse of a right triangle with legs 39 ft will be ...

d² = 39² +39²

d² = 39²(1 +1) = 39²·2

d = √(39²·2) = 39√2

The length of the diagonal is 39√2 feet.

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Additional comment

As you can tell from this answer, the length of the diagonal of any square is √2 times the length one side. Knowing this, you can write down the answer without any further effort.