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 6 , 4 , and 9 , respectively. What is the rectangle's area?

The reqd. Area of rectangle$= 18 \sqrt{5} \cong 40.248$ sq.unit..
In the given right triangle with hypo.=A, we have, by Pythagoras Theorem, ${B}^{2} + {C}^{2} = {A}^{2.} \ldots \ldots \ldots \left(1\right)$.
$A = 6 , C = 4$...[Given] & $\left(1\right) \Rightarrow {B}^{2} = 36 - 16 = 20 \Rightarrow B = \sqrt{20} = 2 \sqrt{5.}$
Hence, the reqd. Area of rectangle $= B \times$ length of side adjacent to $B$$= 2 \sqrt{5} \cdot 9 = 18 \sqrt{5} \cong 18 \cdot 2.236 \cong 40.248$ sq.unit.