Can someone me out with this question? how do you use the pythagorean theorem to answer b?

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

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