Question

The second side of a triangular deck is 5 feet longer than the shortest​ side, and the third side is 5 feet shorter than twice the length of the shortest side. If the perimeter of the deck is 72 ​feet, what are the lengths of the three​ sides?

Answer 1

The lengths of the three sides of the triangular deck are 18 feet, 23 feet, and 31 feet, derived from setting up an equation based on the perimeter and solving for the unknown side lengths.

Step-by-step explanation:

Finding the Lengths of the Sides of a Triangle

Let's denote the length of the shortest side as s. According to the problem, the second side is 5 feet longer than the shortest side, so it can be represented as s + 5. The third side is 5 feet shorter than twice the length of the shortest side, which can be represented as 2s - 5. The perimeter of the triangle is the sum of the lengths of its sides, which in this case totals 72 feet. Hence, we have the following equation:

s + (s + 5) + (2s - 5) = 72

Combining like terms, we get:

4s = 72

Dividing both sides by 4, we find the length of the shortest side:

s = 18 feet

Now we can find the lengths of the other two sides:

• Second side: s + 5 = 18 + 5 = 23 feet
• Third side: 2s - 5 = 2(18) - 5 = 36 - 5 = 31 feet

Therefore, the lengths of the three sides of the triangular deck are 18 feet, 23 feet, and 31 feet.

Answer 2

Answer: the length if the three sides are 31 feet, 23 feet and 18 feet.

Step-by-step explanation:

Let x represent the length of the shortest side of the triangle.

Let y represent the length of the second side of the triangle.

Let z represent the length of the third side of the triangle.

The second side of a triangular deck is 5 feet longer than the shortest​ side. This means that

y = x + 5

The third side is 5 feet shorter than twice the length of the shortest side. This means that

z = 2x - 5

If the perimeter of the deck is 72 ​feet, it means that

x + x + 5 + 2x - 5 = 72

4x = 72

x = 72/4 = 18

z = 2x - 5 = 2 × 18 - 5

z = 36 - 5

z = 31

y = x + 5 = 18 + 5

y = 23