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

24cm

20cm

28cm

7cm

$\frac{88}{7}$

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

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