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 `10`, `3`, and `3`, respectively. What is the rectangle's area?

Answer 1

`"Area"_square =3sqrt(91) ~~28.62` square units

Explanation:

Since `A, B, C` are sides of a right triangle (with `A` the hypotenuse), and
since `abs(A)=10` and `abs(C)=3`
then by the Pythagorean Theorem
`color(white)("XXX")abs(B)=sqrt(10^2-3^2)=sqrt(91)`

Therefore the rectangle has sides with lengths `3` and `sqrt(91)`
and an area of `3xxsqrt(91)=3sqrt(91)`
`color(white)("XXX")`or (using a calculator) approximately `28.62`