Question

A square has side lengths of 9 use the Pythagorean theorem to find the length of the diagonal

Answer 1

Answer:

12.73

Step-by-step explanation:

The diagonal of the square forms the shape of a right angle with two adjacent sides of the square.

The diagonal is the hypotenuse.

Pythagoras theorem states that the square of the hypotenuse is equal to the sum of the square of the other two sides of the triangle:

$d^2 = a^2 + b^2$

where d = hypotenuse = diagonal.

Since the other two sides are equal, then:

$d^2 = a^2 + a^2\\\\d^2 = 2a^2$

The length of the side of the square is 9:

$d^2 = 2 * 9^2 \\\\d^2 = 2 * 81\\\\d^2 = 162\\\\d = \sqrt{162}\\ \\d = 12.73$

The length of the diagonal is 12.73