Question

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

Answer 1

The length of the diagonal of the rectangle is of
`√(58)` units.

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 = √(58)`

The length of the diagonal of the rectangle is of
`√(58)` units.