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# Help!!!

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In triangle ABC, AB = 3, BC = 4, and angle B = 90 degrees. Square DEFG is inscribed in triangle ABC such that D and G are on side AC, E is on side AB and F is on side BC Find the side length of the square.

Jan 20, 2020

#1
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You can use similar triangles!  The side length of the square is 15/7.

Jan 20, 2020
#2
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The answer is not 15/7, sorry. I know you can use similar triangles, but I don't know how to do the problem.

Guest Jan 20, 2020
#3
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In triangle ABC, AB = 3, BC = 4, and angle B = 90 degrees. Square DEFG is inscribed in triangle ABC such that D and G are on side AC, E is on side AB and F is on side BC Find the side length of the square.

Jan 20, 2020
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Thanks! Very rigorous explanation!

Guest Jan 20, 2020
#5
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In triangle ABC, AB = 3, BC = 4, and angle B = 90 degrees.

Square DEFG is inscribed in triangle ABC such that D and G are on side AC, E is on side AB and F is on side BC

Find the side length of the square.

$$\begin{array}{|rclrclrcl|} \hline \tan(A) &=& \dfrac{x}{p} & && & \tan(A) &=& \dfrac{4}{3} \\ &&& \dfrac{x}{p} &=& \dfrac{4}{3}& \\ && &\dfrac{p}{x} &=& \dfrac{3}{4}& \\ && &\mathbf{p} &=& \mathbf{\dfrac{3x}{4}}& \\ \hline \end{array}$$

$$\begin{array}{|rclrclrcl|} \hline \tan(C) &=& \dfrac{x}{q} & && & \tan(C) &=& \dfrac{3}{4} \\ &&& \dfrac{x}{q} &=& \dfrac{3}{4}& \\ && &\dfrac{q}{x} &=& \dfrac{4}{3}& \\ && &\mathbf{q} &=& \mathbf{\dfrac{4x}{3}}& \\ \hline \end{array}$$

$$\begin{array}{|rcll|} \hline p+x+q &=& 5 \\\\ \dfrac{3x}{4}+x+\dfrac{4x}{3} &=& 5 \\\\ x*\left( \dfrac{3}{4}+1+\dfrac{4}{3} \right) &=& 5 \\ x* \dfrac{37}{12} &=& 5 \\\\ x &=& 5*\dfrac{12}{37} \\\\ x &=& \dfrac{60}{37} \\\\ \mathbf{x} &=& \mathbf{1.\overline{621}} \\ \hline \end{array}$$

Jan 21, 2020
edited by heureka  Jan 21, 2020