Question

If the sides of a square measure 9.3 units the.find the length of the diagonal

Answer 1

Approximately 13.1521 units.

Explanation:

To find the diagonal, we can use the Pythagorean Theorem.

Since the figure is a square, all four sides are equivalent. A square also has four right angles. Therefore, we can use the Pythagorean Theorem to find the diagonal d. Therefore:

`a^2+b^2=c^2`

Substitute 9.3 for a and b, and let c equal d:

`(9.3)^2+(9.3)^2=d^2`

Instead of squaring, add the like-terms:

`2(9.3)^2=d^2`

Take the square root of both sides:

`d=√(2(9.3)^2)`

Expand:

`d=√(2)\cdot√((9.3)^2)`

The right cancels:

`d=\sqrt2\cdot(9.3)\\d=9.3\sqrt2\\d\approx13.1521\text{ units}`