MATH SOLVE

2 months ago

Q:
# Please help on this pythagorean question, find x.

Accepted Solution

A:

Answer:x = 4Step-by-step explanation:Since the triangle is right use Pythagoras' identity to solve for xThe 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 sidex² + 6x + 9 + 16(x+ 2)² = 625x² + 6x + 9 + 16(x² + 4x + 4) = 625x² + 6x + 9 + 16x² + 64x + 64 = 625 ← simplify left side17x² + 70x + 73 = 625 ( subtract 625 from both sides )17x² + 70x - 552 = 0 ← in standard formwith a = 17, b = 70, c = - 552Using the quadratic formula to solve for xx = ( - 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 ) / 34x = [tex]\frac{-70-206}{34}[/tex] = - 8.1176.... or x = [tex]\frac{-70+206}{34}[/tex] = 4However, x > 0 ⇒ x = 4Hencex + 3 = 4 + 3 = 7 and 4(4 + 2) = 24The triangle is a 7- 24- 25 right triangle