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

Explanation:

Step1: Let the length of the shortest side be $x$ feet.

The second - side length is $2x$ feet (since one side is twice the length of the shortest side), and the third - side length is $(x + 13)$ feet (since the third side is 13 feet more than the length of the shortest side).

Step2: Set up the perimeter equation.

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

Step3: Combine like - terms.

Combining the $x$ terms on the left - hand side gives $(1 + 2+1)x+13=145$, which simplifies to $4x+13 = 145$.

Step4: Isolate the variable term.

Subtract 13 from both sides of the equation: $4x+13−13=145−13$, resulting in $4x=132$.

Step5: Solve for $x$.

Divide both sides of the equation by 4: $\frac{4x}{4}=\frac{132}{4}$, so $x = 33$.

Answer:

33 feet