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 `7`, `6`, and `15`, respectively. What is the rectangle's area?

Answer 1

`15sqrt(13)`

Explanation:

The above (not to scale) picture contains the information given in the problem. In many geometry problems, drawing a picture is a good way to start.

The area of the rectangle is the product of the lengths of its sides, in this case `15B`. To solve for `B`, we can use the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of its legs. In this case, that translates to `A^2 = B^2 + C^2`

Substituting in the given values for `A` and `C`, we obtain

`49 = B^2 + 36`

`=> B^2 = 13`

`=> B = sqrt(13)`

Thus the area of the rectangle is `15sqrt(13)`