Question

The diagonal of a square is x units. What is the area of the square in terms of x? square units square units 2x square units square units

Answer 1

Option A: 1/2 x^2

Explanation:

Answer 2

For this case we have that by definition, if we draw the diagonal of a square two rectangular triangles are formed. If the diagonal measures "x", then the Pythagorean theorem is fulfilled:

`l ^ 2 + l ^ 2 = x ^ 2`

Where:

l: It's the side of the square.

`2l ^ 2 = x ^ 2\\l ^ 2 = \frac {x ^ 2} {2}`

We know that the area of a square is given by:

`A = l ^ 2`

So, the area is:

`A = \frac {x ^ 2} {2}`

Answer:

`A = \frac {x ^ 2} {2}`