The perimeter of a triangle is 50 cm. One side of the triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.

Options

A. `20 sqrt(30) cm^(2)`
B. `30 sqrt(30) cm^(2)`
C. `40 sqrt(30) cm^(2)`
D. `50 sqrt(30) cm^(2)`

Answer

A

Explanation

Let the smallest side be x cm.
Then, the other sides are (x + 4) cm and (2x - 6) cm.
`therefore" "x+(x+4)+(2x-6)=50 rArr 4x = 52 rArr x = 13`.
Thus, the sides are 13 cm, 17 cm and 20 cm.