Answer:
the length of the shorter leg : 7 cm
the length of the longer leg : 24 cm
the length of the Hypotenuse : 25 cm
Step-by-step explanation:
a = 3b + 3
c = 3b + 4
and we know the general Pythagoras :
c² = a² + b²
(3b + 4)² = (3b + 3)² + b²
9b² + 24b + 16 = 9b² + 18b + 9 + b²
24b + 16 = 18b + 9 + b²
6b + 7 = b²
b² - 6b - 7 = 0
the general solution to such a quadratic equating is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case
x is called b.
a = 1
b = -6
c = -7
b = (6 ± sqrt((-6)² - 4×1×-7))/(2×1) = (6 ± sqrt(36 + 28))/2 =
= (6 ± sqrt(64))/2 = (6 ± 8)/2
b1 = (6+8)/2 = 14/2 = 7 cm
b2 = (6-8)/2 = -2/2 = -1 cm
a negative number did not make sense for a side length, so,
b = 7 cm
is our solution for one leg.
a = 3b + 3 = 3×7 + 3 = 24 cm
c = 3b + 4 = 25 cm
