Question

Please help!! Find A

Answer 1

Answer:

  (5/2)√13 ≈ 9.0139

Step-by-step explanation:

The longer hypotenuse is found using the Pythagorean theorem as ...

  $\sqrt{8^2+12^2}=\sqrt{208}=4\sqrt{13}$

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.

  $A=\dfrac{5}{8}\cdot 4\sqrt{13}= \dfrac{5\sqrt{13}}{2}$