Question

"john is developing a game that contains a triangular game board. The perimeter of the triangular board is 36 inches. Find the length of the three sides if the middle length side is 2 inches greater than the smallest​ side, and the longest side is 2 inches less than twice the length of the smallest side."

Answer 1

Answer:

Smallest side: 9 inches,

Middle length: 11 inches,

Longest side: 16 inches.

Step-by-step explanation:

Let x represent the length of the smaller side of the triangular board.

We have been given that the middle length side is 2 inches greater than the smallest​ side, so the middle length would be $x+2$ inches.

Since the longest side is 2 inches less than twice the length of the smallest side. So the length of the longest side would be $2x-2$.

We are also told that the perimeter of the triangular board is 36 inches. We know that perimeter of triangle is equal to sum of its three sides, so we can represent this information in an equation as:

$x+x+2+2x-2=36$

Let us solve for x.

$4x+2-2=36\\\\4x=36$

$\frac{4x}{4}=\frac{36}{4}$

$x=9$

Therefore, the length of the smallest side would be 9 inches.

The side with middle length would be $x+2\Rightarrow9+2=11$.

The length of the longest side would be $2x-2\Rightarrow2(9)-2=18-2=16$

Therefore, the longest side would be 16 inches.