A gymnast performs a tumbling run along the diagonal of a square mat with sides that are 35 feet long. What distance does the gymnast tumble?

1 Answer
mason m
Nov 20, 2015

35sqrt2 feet

Explanation:

Refer to the following picture of a square with a diagonal drawn in:

![mathamazement.com](useruploads.socratic.org)

When the diagonal is drawn, two triangles with degree measures of 45˚,45˚,90˚ are created. It is very important in geometry to remember that in this situation, where a triangle has those two angle measurements, the hypotenuse is always sqrt2 times larger than the other two sides, which are congruent.

For example, in a 45˚,45˚,90˚ triangle where the two shortest sides are 11, the hypotenuse is 11sqrt2.

This is almost identical to your problem. Each side of the square is 35, so the diagonal of the square, which is the hypotenuse of the 45˚,45˚,90˚ triangle is just sqrt2xx35 feet=35sqrt2 feet.

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