Question

14. What is the length of a diagonal of rectangle EFGH? Show your work

Answer 1

Answer:

The length of the diagonal of the rectangle is of $\sqrt{58}$ units.

Step-by-step explanation:

Pythagorean theorem:

The square of the hypothenuse h is equal to the sum of the squares of sides a and b, that is:

$h^2 = a^2 + b^2$

Diagonal of a rectangle:

The diagonal is the hypothenuse, while the sides are a and b.

In this question:

The height has coordinates are y = 9 and y = 12, so the height is $a = 12 - 9 = 3$

The length has coordinates at $x = -6, x = -13$, so the length is $b = -6 - (-13) = 7$

Diagonal:

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

$d^2 = 3^2 + 7^2$

$d^2 = 9 + 49$

$d^2 = 58$

$d = \sqrt{58}$

The length of the diagonal of the rectangle is of $\sqrt{58}$ units.