MathDB
Annoying Areas

Source: 2019 AMC 10B #15

February 14, 2019
AMCAMC 10AMC 10 B

Problem Statement

Two right triangles, T1T_1 and T2T_2, have areas of 1 and 2, respectively. One side length of one triangle is congruent to a different side length in the other, and another side length of the first triangle is congruent to yet another side length in the other. What is the square of the product of the third side lengths of T1T_1 and T2T_2?
<spanclass=latexbold>(A)</span>283<spanclass=latexbold>(B)</span>10<spanclass=latexbold>(C)</span>323<spanclass=latexbold>(D)</span>343<spanclass=latexbold>(E)</span>12<span class='latex-bold'>(A) </span>\frac{28}3\qquad<span class='latex-bold'>(B) </span>10\qquad<span class='latex-bold'>(C) </span>\frac{32}3\qquad<span class='latex-bold'>(D) </span>\frac{34}3\qquad<span class='latex-bold'>(E) </span>12