If one side of a triangle is 7 with its perimeter equal to 18, and area equal to 108 , then the other two sides are:

Answer: Option D

a = 7 cm
2S = a + b + c = 18
S = 9 cm
a + b + c = 18
7 + b + c = 18
b + c = 11
b = 11 - c
$$\begin{array}{rl}& \Delta =\sqrt{\text{S}\left(\text{S}-\text{A}\right)\left(\text{S}-\text{B}\right)\left(S-\text{C}\right)}\\ & \Delta =\sqrt{9\left(9-7\right)\left(9-11-\text{C}\right)\left(9-\text{C}\right)}\\ & \Delta =\sqrt{9\times 2\left(\text{C}-2\right)\left(9-\text{C}\right)}\\ & \sqrt{108}=\sqrt{18\left(\text{C}-2\right)\left(9-\text{C}\right)}\end{array}$$
6 = 9C - C² - 18 + 2C
24 = C² + 11C
C² - 11C + 24 = 0
C² - 8C - 3C + 24 = 0
C(C - 8) - 3(C - 8) = 0
(C - 3)(C - 8) = 0
C = 3, 8
B = 8, 3
Side = 3, 8