Question

A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of `5`, `4`, and `11`, respectively. What is the rectangle's area?

Answer 1

The area of the rectangle is `33`.

Explanation:

From the data given we can draw the following shape:

Since the triangle is right angled, we can determine the length of B using the Pythagorean theorem.

`B^2+C^2=A^2`

`B^2+4^2=5^2`

`B^2+16=25`

Subtract `16` from each side.

`B^2=25-16`

`B^2=9`

Determine the square root.

`B=3`

Since we know that `B=3` and that the side adjacent to `B` is `11`, the area of the rectangle can be calculated using the formula:

`A=lxxh`

where `l=`length (`11`) and `h=`height (in this case: `B=11`)

`A=3xx11`

`A=33`