Answer:
UN = 7
Step-by-step explanation:
Using Pythagoras' identity on the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
(4x - 3)² = (3x + 3)² + x² ← distribute both sides
16x² - 24x + 9 = 9x² + 18x + 9 + x² ← simplify
16x² - 24x + 9 = 10x² + 18x + 9 ( subtract 10x² + 18x + 9 from both sides )
6x² - 42x = 0 ← factor out 6x from each term
6x(x - 7) = 0
Equate each factor to zero and solve for x
6x = 0 ⇒ x = 0
x - 7 = 0 ⇒ x = 7
However, x > 0 ⇒ x = 7
Hence UN = x = 7 and SU = 4x - 3 = (4 × 7) - 3 = 28 - 3 = 25
