Question

A square has 4 sides of equal length. If a diagonal of the square is `5sqrt2`, what is the length of each side?

Answer 1

`5" units"`

Explanation:

Let the side of the square be x

Now apply `color(blue)"Pythagoras' theorem"` to the right triangle formed by the diagonal and 2 sides of the square.

`rArrx^2+x^2=(5sqrt2)^2`

`rArr2x^2=50`

divide both sides by 2

`(cancel(2) x^2)/cancel(2)=50/2`

`rArrx^2=25`

take the square root of both sides.

`sqrt(x^2)=+-sqrt25=+-5`

Since x > 0 , then x = 5

Thus the square has a side of 5 units.

Answer 2

Length of each side is `5`.

Explanation:

If we draw a diagonal of a square, whose side is `s`, we get the length of diagonal from Pythagoras theorem as

`sqrt(s^2+s^2)=sqrt(2s^2)=ssqrt2`

Now in given case diagonal of the square is `5sqrt2`.

Hence, length of each side is `5`