Answer:
Step-by-step explanation:
Pythagoras simply says that for a right triangle, the sum of the squares of the two shorter legs will equal the square of the hypotenuse.
a² + b² = c²
in this case a = x
b = x + 2
c = x + 3
x² + (x + 2)² = (x + 3)²
x² + (x + 2)² = (x + 3)²
x² + (x² + 4x + 4) = (x² + 6x + 9)
2x² + 4x + 4 = x² + 6x + 9
x² - 2x - 5 = 0
quadratic formula
x = (2 ±√(2² - 4(1)(-5))) / (2(1))
x = (2 ± √24) / 2
a negative length does not make sense so
x = 1 + √6
x ≈ 3.4
x + 2 ≈ 5.4
x + 3 ≈ 6.4
