Expert: Sherman D. - 8/5/2006

Question
In a right triangle, the hypotenuse equals 50 feet, the base is unknown, and the height is 10 feet more than the base. What is the value of the base?

Answer
a^2 + b^2 = c^2
a = base
c = 50
b = height a + 10

a^2 + (a + 10)^2 = 50^2
a^2 + ((a + 10)(a + 10)) = 2500
a^2 + (a^2 + 10a + 10a + 100) = 2500
a^2 + a^2 + 20a + 100 = 2500
2a^2 + 20a + 100 = 2500
2a^2 + 20a - 2400
a^2 + 10a - 1200 = 0

x = (-b ± sqrt(b^2 - 4ac))/2a

x = (-10 ± sqrt(10^2 - 4(1)(-1200)))/(2(1))
x = (-10 ± sqrt(100 + 4800))/2
x = (-10 ± sqrt(4900))/2
x = (-10 ± 70)/2
x = (-80/2) or (60/2)
x = -40 or 30

or in this case

a = 30

b = 30 + 10
b = 40

Height = 40ft
BASE = 30ft