# 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?

Nov 20, 2015

$35 \sqrt{2}$ feet

#### Explanation:

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

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 $\sqrt{2}$ 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 $11 \sqrt{2}$.

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 $\sqrt{2} \times 35$ feet$= 35 \sqrt{2}$ feet.