Question

The diagonal of a square is x units. What is the area of the square in terms of x?

Answer 1

`(1)/(2)` x²

Explanation:

let the length of the side be l

Then using Pythagoras' identity on the right triangle formed by the diagonal ( hypotenuse ) and the 2 sides

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

l² + l² = x²

2l² = x² ( divide both sides by 2 )

l² =
`(1)/(2)` x² ( since A of square = l² )