Problem 131

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Problem 131: (2019 AMC 10b, 15)

Right triangles $T_1$ and $T_2$, have areas of 1 and 2, respectively. A side of $T_1$ is congruent to a side of $T_2$, and a different side of $T_1$ is congruent to a different side of $T_2$. What is the square of the product of the lengths of the other (third) sides of $T_1$ and $T_2$? $\textbf{(A) }\frac{28}{3}\qquad$ $\textbf{(B) }10\qquad$ $\textbf{(C) }\frac{32}{3}\qquad$ $\textbf{(D) }\frac{34}{3}\qquad$ $\textbf{(E) }12$

Solution

Exercise 131: Solution

Right triangles $T_1$ and $T_2$ have areas $2$ and $3$, respectively. A side of $T_1$ is congruent to a side of $T_2$, and a different side of $T_1$ is congruent to a different side of $T_2$. What is the square of the product of the lengths of the other (third) sides of $T_1$ and $T_2$?

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