Answer:
x = 4
Step-by-step explanation:
Since the triangle is right use Pythagoras' identity to solve for x
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
(x + 3)² + (4(x + 2))² = 25² ← expand parenthesis on left side
x² + 6x + 9 + 16(x+ 2)² = 625
x² + 6x + 9 + 16(x² + 4x + 4) = 625
x² + 6x + 9 + 16x² + 64x + 64 = 625 ← simplify left side
17x² + 70x + 73 = 625 ( subtract 625 from both sides )
17x² + 70x - 552 = 0 ← in standard form
with a = 17, b = 70, c = - 552
Using the quadratic formula to solve for x
x = ( - 70 ± [tex]\sqrt{70^2-(4(17)(-552)}[/tex] ) / 34
= ( - 70 ± [tex]\sqrt{4900+37536}[/tex] ) / 34
= - 70 ± [tex]\sqrt{42436}[/tex] ) / 34
= - 70 ± 206 ) / 34
x = [tex]\frac{-70-206}{34}[/tex] = - 8.1176....
or x = [tex]\frac{-70+206}{34}[/tex] = 4
However, x > 0 ⇒ x = 4
Hence
x + 3 = 4 + 3 = 7 and
4(4 + 2) = 24
The triangle is a 7- 24- 25 right triangle
