Question

What is the length of the side of a square whose diagonal is 10?

Answer 1

Draw a diagram to represent your situation.

Explanation:

Since we're dealing with a square, all side lengths measure the same thing. Furthermore, the angle B and D are right, therefore allowing us to use pythagorean theorem to find the value of a.

`color(blue)(a^2 + b^2 = c^2`

Where `aand b` are the right containing sides

Since `aandb` are equal,we consider them as `a`

`c` is the Hypotenuse of the right-triangle

The diagonal is the Hypotenuse `c`

`rarra^2 + a^2 = 10^2`

`rarr2a^2 = 100`

`rarra^2 = 50`

`rarra = sqrt(50)`

`color(green)(rArra=sqrt(25*2)=5sqrt2`

So, the side lengths measure `5sqrt(2) or 7.07` units each.

Hopefully this helps!