[Math] Explain logic..construct a square PQRS when the sum of its diagonal and side is 8cm.

geometry

In the book question is solved by..
Making triangle with 8cm base and 8 cm perpendicular.
Then difference of hypotenuse n base is used to draw square.

What's the logic behind this?

Best Answer

Say the square had side $s$. The diagonal has length $\sqrt 2 s$ so we have $$s+\sqrt 2 s = 8 \implies s(\sqrt 2 +1)=8\implies s=\frac 8{\sqrt 2 +1}=8\times (\sqrt 2 -1)$=8\sqrt 2 - 8$$

Now, in your (isosceles) right triangle, the hypotenuse is $8\sqrt 2$ and the side is $8$ so the desired claim follows at once.

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