Answer:
x = 1
Step-by-step explanation:
Assuming you require to calculate the value of x
Since the triangle is right use Pythagoras' theorem
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
(x + 1)² + (x + 3)² = (2[tex]\sqrt{5}[/tex])² ← expand and simplify left side
x² + 2x + 1 + x² + 6x + 9 = 20
2x² + 8x + 10 = 20 ( subtract 20 from both sides )
2x² + 8x - 10 = 0 ← in standard form
Divide through by 2
x² + 4x - 5 = 0 ← factor the quadratic
(x + 5)(x - 1) = 0
Equate each factor to zero and solve for x
x + 5 = 0 ⇒ x = - 5
x - 1 = 0 ⇒ x = 1
However, x > 0 ⇒ x = 1
