Solve Pythagoras problem solving

Question

A rectangular piece of paper,10cm by 24cm, is folded so that a pair of diagonally opposite corners coincide. Find the length of the crease.

x^2=(24-x)^2+10^2

Answer 1

Hint : Try To fold Paper, and You'll get it

You can then continue with @ir7 's answer

Note : The Diagram is not upto the scale

Answer 2

Hint:

Let $ABCD$ be the rectangle (length of $AB$ be $24$ and length of $BC$ be $10$) , and $MN$ be the crease segment, with $M$ on segment $AB$ and $N$ on segment $CD$, resulting from forcing opposite corners $A$ and $C$ to overlap.

Consider right triangle $CMB$.

Denoting length of segment $MB$ by $x$ and noting that length of segment $CM$ is $24-x$, by Pythagoras theorem we get:

$$ (24-x)^2 = x^2 +10^2.$$

Once we have $x$, length of $MN$ is easy to obtain.