Question

Use the Pythagorean Theorem to find an approximate value of x

that makes the diagram true.
(3x+4)
(3x)
(2x+1)

Answer 1

Explanation:

Hypotenuse² =base² + altitude²

(3x + 4)² = (2x + 1)² + (3x)²

{Use (a+b)² = a² + 2ab + b²}

(3x)² + 2*3x+4 + 4² = (2x)² + 2*2x*1 + 1² + 9x²

9x² + 24x + 16 = 4x² + 4x + 1 + 9x²

9x² + 24x + 16 = 13x² + 4x + 1

0 = 13x² + 4x + 1 - 9x² - 24x - 16

13x² - 9x² + 4x - 24x +1 - 16 = 0

4x² - 20x - 15 = 0

a = 4 ; b =-20 ; c = -15

D = b² - 4ac = (-20)² - 4*4*(-15) = 400 + 240 = 640

√D = √640 = 25.30

`x=(-b+√(D))/(2a) \ ; \ x=(-b-√(D))/(2a)\\\\\\x=(20+25.30)/(2*4) \ ; \ x=(20-25.30)/(2*4)\\\\\\x=(45.30)/(8) \ ; \ x =(-5.30)/(8)\\\\`

x = 5 .66 ; x = -0.66

Ignore x = -0.66 as length of a side cannot be negative

Answer : x = 5.66