Answer:
x = 2√30, y = 2√21
Step-by-step explanation:
You can create the following equations:
(1) from the left triangle with sides x, y and 6:
y² + 6² = x²
(2) from the right triangle with sides y, 14 and... lets call it z:
y² + 14² = z²
(3) from the big triangle:
x² + z² = 20²
(4) Combine (2) and (3) to eliminate z:
x² + y² + 14² = 20²
combine (1) and (4) to eliminate x:
y² + 6² + y² + 14² = 20²
simplify
2y² = 20² - 6² - 14² = 168
y² = 84
y = √84 = 2√21
x² = y² + 6² = 84 + 36 = 120
x = √120 = 2√30
