Polygons and Circles Question 7

In square $ABCD$ shown below, $\overline{AC}$ is a diagonal and the length of $\overline{BC}$ is 75 feet. Which of the following quantities is NOT a rational number?

The perimeter of

ABCD

, in feet

The area of

ABCD

, in square feet

The length of

\overline{AB}

, in feet

The length of

\overline{AC}

, in feet

The measure of

\angle{CAD}

, in degrees

Approach

The triangles in a square are $45-45-90$ special right triangles with ratios $1:1:\sqrt{2}$ . The diagonal of our square will be $75\sqrt{2}$ , which is an irrational number.