The sides of a triangle are(x + 4)cm, xcm and (x – 4)cm, respectively If…

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

Correct Answer: Option A

Explanation

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