Answer:
(x - y) = 9
Step-by-step explanation:
**Note: we cannot use similar triangle proportionality, as ΔABC is NOT a right triangle**
Using Pythagoras' Theorem a² + b² = c²
(where a and b are the legs and c is the hypotenuse of a right triangle)
Create equations for both smaller interior right triangles using Pythagoras' Theorem:
Larger right triangle
CD² + x² = 17²
⇒ CD² = 17² - x²
Smaller right triangle
CD² + y² = 10²
⇒ CD² = 10² - y²
Equate equations:
CD² = CD²
⇒ 17² - x² = 10² - y²
Given:
AB = 21 and AB = x + y
⇒ x + y = 21
⇒ y = 21 - x
Substitute y = 21 - x into 17² - x² = 10² - y² and solve for x:
⇒ 17² - x² = 10² - (21 - x)²
⇒ 17² - x² = 10² - (441 - 42x + x²)
⇒ 17² - x² = 10² - 441 + 42x - x²
⇒ 289 = 100 - 441 + 42x
⇒ 630 = 42x
⇒ x = 630 ÷ 42
⇒ x = 15
Substitute found value for x into y = 21 - x and solve for y:
⇒ y = 21 - 15 = 6
Finally, substitute found values for x and y into (x - y):
⇒ x - y = 15 - 6 = 9
