The sides of a triangle are(x + 4)cm, xcm and (x - 4)cm, respectively If the cosine of the largest angle is \(\frac{1}{5}\), find the value of x
A
24cm
B
20cm
C
28cm
D
7cm
E
\(\frac{88}{7}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
2 - a2 + c2 - 2a Cos B
Cos B = \(\frac{a^2 + c^2 - b^2}{2ac}\)
\(\frac{1}{5}\) = \(\frac{x^2 + ?(x - 4)^2 - (x + 4)^2}{2x (x - 4)}\)
\(\frac{1}{5}\)= \(\frac{x(x - 16)}{2x(x - 4)}\)
\(\frac{1}{5}\) = \(\frac{x - 16}{2x - 8}\)
= 5(x - 16)
= 2x - 8
3x = 72
x = \(\frac{72}{3}\)
= 24
Source: Myschool Past Questions Archive (Record #32433)