+41 Right triangle ABC has legs AC=21 and BC=28 and hypotenuse AB=35 . A square is inscribed in triangle ABC as shown below. Find the side length of the square.
+26388 Right triangle ABC has legs AC=21 and BC=28 and hypotenuse AB=35 .
A square is inscribed in triangle ABC as shown below.
Find the side length of the square.
\(\begin{array}{|rcll|} \hline \mathbf{\dfrac{AC-x}{x}} & \mathbf{=} & \mathbf{\dfrac{AC}{BC}} \quad & | \quad AC=21, ~BC=28 \\\\ \dfrac{21-x}{x} & = & \dfrac{21}{28} \\\\ \dfrac{21-x}{x} &=& \dfrac{3}{4} \\\\ (21-x)\cdot 4 &=& 3x \\ 21\cdot 4-4x &=& 3x \\ 84&=& 3x+4x \\ 84&=& 7x \\ 12&=& x \\ \mathbf{x} & \mathbf{=} & \mathbf{12} \\ \hline \end{array}\)
The side length of the square is 12
