Question

Will give brainliest to correct answer.

Answer 1

It equals 2 so that is the answer

Answer 2

It's going to be kind of crazy, but you need to use Pythagorean's Theorem for this.  That will look like this: $(2 \sqrt{x} +1)^2=( \sqrt{x} +1)^2+(2 \sqrt{x} )^2$.  FOIL out the left side to get $4x+4 \sqrt{x} +1$.  FOIL out the first of the 2 expressions on the right to get $x+2 \sqrt{x} +1$,  and the second of the 2 to get 4x.  Our equation now looks like this:  $4x+4 \sqrt{x} +1=x+2 \sqrt{x} +1+4x$.  Combine like terms to get an equation that still has square roots in it that we have to deal with:  $4x-x-4x=-2 \sqrt{x}$  and $x=2 \sqrt{x}$.  We will square both sides to get rid of the square root sign.  $x^{2} =2x$.  This is a polynomial now that can be factored to solve for x.  Bring the 2x over by subtraction and set the polynomial equal to 0.  $x^{2} -2x=0$.  Factor out an x, leaving us with  x(x-2)=0.  That means that x = 0 or x - 2 = 0 and x = 2.  Of course if we are solving for the length of a side we know it can't have a side length of 0, so it must have a side length that is a multiple of 2.  x = 2