Question

the perimeter of a triangle is 97 feet. one side of the triangle is eleven feet more than the smallest side. the third side is six feet more than twice the smallest side. find the lengths of all sides.

Explanation:

Step1: Let smallest side be $x$.

Let sides be $x$, $x + 11$, $2x+6$.

Step2: Set up perimeter equation.

$x+(x + 11)+(2x+6)=97$.

Step3: Simplify left - hand side.

$4x+17 = 97$.

Step4: Solve for $x$.

$4x=97 - 17=80$, so $x = 20$.

Step5: Find other sides.

$x + 11=20+11 = 31$, $2x+6=2\times20 + 6=46$.

Answer:

20 feet, 31 feet, 46 feet