Question

The second side of a triangular deck is 4 feet longer than the shortest​ side, and the third side is 4 feet shorter than twice the length of the shortest side. if the perimeter of the deck is 56 ​feet, what are the lengths of the three​ sides?

Answer 1

To find the lengths of the sides of a triangular deck given the perimeter is 56 feet, we set up an equation based on the relationships between the sides. Solving the equation shows the shortest side is 14 feet, the second side is 18 feet, and the third side is 24 feet.

Step-by-step explanation:

The question involves finding the lengths of the sides of a triangle given the perimeter and the relationships between the sides. Let's define the shortest side as x. According to the question, the second side is 4 feet longer than the shortest side, so it can be represented as x + 4 feet. The third side is described as 4 feet shorter than twice the length of the shortest side, which can be written as 2x - 4 feet. The perimeter of the triangle, which is the sum of the lengths of all sides, is given as 56 feet. Therefore, the equation to find the sides is:

x + (x + 4) + (2x - 4) = 56

Solving this equation will provide the length of the shortest side, and consequently, the lengths of the other two sides can also be determined.

Step-by-step:

1. Write down the equation for the perimeter: x + (x + 4) + (2x - 4) = 56.
2. Simplify the equation: 4x = 56.
3. Divide both sides by 4 to find x: x = 14 feet.
4. Calculate the second side: x + 4 = 18 feet.
5. Calculate the third side: 2x - 4 = 24 feet.

Therefore, the lengths of the three sides of the triangular deck are 14 feet, 18 feet, and 24 feet.

Answer 2

Let's assume

first side as shortest side

and shortest side =x

we are given

the second side of a triangular deck is 4 feet longer than the shortest​ side

so, second side is

`=x+4`

the third side is 4 feet shorter than twice the length of the shortest side

so, third side is

`=2x-4`

now, we are given

perimeter =56

so,

first side + second side + third side =56

we get

`x+x+4+2x-4=56`

`x+x+2x=56`

now, we can solve for x

`4x=56`

`x=14`

so,

first side is 14 feet

Second side is:

`=14+4`

`=18 feet`

Third side is:

`=2*14-4`

`=24feet`