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.

\(\frac{88}{7}\)

Correct answer is A

< B is the largest since the side facing it is the largest, i.e. (x + 4)cm

Cosine B = \(\frac{1}{5}\)

= 0.2 given

b2 - 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