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`, `4`, and `1`, respectively. What is the rectangle's area?

Answer 1

The rectangle's area is `sqrt(33)` or `5.74`

Explanation:

Above is a drawing of the situation in question.

Since we have two sides of a right triangle, we can use the Pythagorean theorem to calculate the length of side B.

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

Be sure to note that a and b here refer to the smaller sides of the triangle and the c refers to hypotenuse, which is different from the letters in our diagram!

`4^2+b^2=7^2`

`16+b^2=49`

`b^2=33`

`b=sqrt(33)`

Now, to calculate the area of the rectangle, we must multiple its length by its width. Side B is its length and we already know its width is 1, and since any number multiple by 1 is just itself, the area of the rectangle is `sqrt(33)`, or `5.74`