What is the value of x in the diagram?

x=5

Step-by-step explanation:

Since this is a right triangle, we can use the pythagorean theorem

a^2 + b^2 = c^2

x^2+ ( 2x+2)^2 = (2x+3)^2

FOIL the squared terms

x^2 +(4x^2 + 4x+4x+4) = 4x^2 + 6x+6x +9

Combine like terms

5x^2+8x +4 = 4x^2 +12x +9

Subtract  4x^2 +12x +9 from each side

5x^2+8x +4  -4x^2 -12x -9= 4x^2 +12x +9-4x^2 -12x -9

x^2 -4x -5 =0

Factor

(x-5) (x+1) = 0

Using the zero product property

x=5   x=-1

But x cannot be negative or we would have negative length

x=5

34

step-by-step explanation: