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

Let

b------> the length side of a square

we know that

the area of a square is equal to

`A=b^(2)`

Find the length side of the diagonal applying the Pythagoras Theorem

`d^(2)=b^(2)+b^(2)`

`d^(2)=2b^(2)`

`d=b√(2)\ units`

Remember that

`d=x\ units` -----> given problem

substitute

`d=b√(2)\ units`

`x=b√(2)\ units`

Solve for b

`b=(x√(2))/(2)\ units`

Substitute in the formula of area

`A=((x√(2))/(2))^(2)`

`A=(x^(2))/(2)\ units^(2)`

therefore

the answer is

`(x^(2))/(2)\ units^(2)`