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# ​ help

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122
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help

Jun 19, 2020

#1
+245
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Use the Pythgorean Thearom and find the hypotenuse remember a^2+b^2=c^2

divide RQ by 2 and divide PQ by 2 then use the Pythgorean Thearom to find ZX

Jun 19, 2020
#2
+8342
0

Notice that \(\triangle RYX \sim \triangle XZQ\) by AA postulate.

Let x be the side length of the square. Then

\(ZQ = 12-x\\ RY=8-x\\ YX=x\\ XZ=x\)

By similar triangles,

\(\dfrac{RY}{YX} = \dfrac{XZ}{ZQ}\\ \dfrac{8-x}{x}=\dfrac{x}{12-x}\)

Solving this equation gives the required answer.

Ans: Side length = 24/5.

As an exercise, you can try to show that when PQ = a, PR = b, the side length of the square is \(\dfrac{ab}{a + b}\).

Jun 19, 2020