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 `18`, `12`, and `9`, respectively. What is the rectangle's area?

Answer 1

`6sqrt5 ≈ 120.75 " square units "`

Explanation:

area of rectangle = length`xx " breadth " = 9B`
and require to find B.

Since right triangle can use`color(blue)" Pythagoras's theorem "`

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

hence `B^2 = A^2 - C^2 = 18^2 - 12^2 = 180`

since `B^2 = 180 rArr B = sqrt180 = 6sqrt5`

thus area of rectangle = `9sqrt180 ≈ 120.75 " square units "`