Answer:
(5/2)√13 ≈ 9.0139
Step-by-step explanation:
The longer hypotenuse is found using the Pythagorean theorem as ...
[tex]\sqrt{8^2+12^2}=\sqrt{208}=4\sqrt{13}[/tex]
The right triangles are AA similar, and vertical sides correspond. Their ratio, smaller/larger is 5/8. That means the hypotenuse of the smaller triangle, A, is 5/8 of the hypotenuse of the larger one.
[tex]A=\dfrac{5}{8}\cdot 4\sqrt{13}= \dfrac{5\sqrt{13}}{2}[/tex]
