Answer:
x ≈ 4.5
Step-by-step explanation:
Let y represent the hypotenuse of the smaller triangle. The Pythagorean theorem tells us the sum of the squares of the legs is equal to the square of the hypotenuse. This lets us write two equations:
1² +2² = y²
y² +x² = 5²
Using the first equation to substitute for y² in the second equation, we get ...
1² +2² +x² = 5²
1 + 4 + x² = 25 . . . . compute the squares
x² = 25 -5 = 20 . . . subtract 5
x = √20 ≈ 4.472 . . . . take the square root
x ≈ 4.5
