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

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?

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.