Question

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?

Answer 1

`35sqrt2` 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 `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.