Question

a flower bed is in the shape of a triangle with one side twice the length of the shortest side and the third side is 13 feet more than the length of the shortest side. find the dimensions if the perimeter is 145 feet. what is the length of the shortest side? the length of the shortest side is 33 feet. what is the length of the second side? the length of the second side is 66 feet. what is the length of the third side? the length of the third side is

Explanation:

Step1: Define the sides

Let the length of the shortest side be $x$ feet. Then the second - side is $2x$ feet and the third side is $x + 13$ feet.

Step2: Set up the perimeter equation

The perimeter of a triangle is the sum of its sides. So, $x+2x+(x + 13)=145$.

Step3: Simplify the left - hand side of the equation

Combine like terms: $x+2x+x+13 = 4x+13$. So the equation becomes $4x+13 = 145$.

Step4: Solve for $x$

Subtract 13 from both sides: $4x=145 - 13=132$. Then divide both sides by 4: $x=\frac{132}{4}=33$.

Step5: Find the length of the second side

The second side is $2x$. Substitute $x = 33$ into it, $2x=2\times33 = 66$.

Step6: Find the length of the third side

The third side is $x + 13$. Substitute $x = 33$ into it, $x+13=33 + 13=46$.

Answer:

The length of the shortest side is 33 feet.
The length of the second side is 66 feet.
The length of the third side is 46 feet.