Question

If the area of a square is 12cm^2 what is the product of its diagonals?

Answer 1

The product of the diagonals of a square with area `12 cm^2` is `24 cm`

Explanation:

If the area of a square is 12
each side has a length of `sqrt(12)`

The product of the diagonals is the same as the square of a diagonal (since the diagonals of a square are equal in length).

By the Pythagorean Theorem:
the square of a diagonal = sum of the squares of the two sides
`color(white)("XXXX")` `=(sqrt(12))^2 +(sqrt(12))^2`

`color(white)("XXXX")` `=24`