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 28 feet more than the length of the shortest side. find the dimensions if the perimeter is 160 feet.
a = ft (shortest side)
b = ft (second side)
c = ft (third side)

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 $(x + 28)$ feet.

Step2: Set up the perimeter equation

The perimeter of a triangle is the sum of its sides. So, $x+2x+(x + 28)=160$.

Step3: Simplify the left - hand side of the equation

Combining like terms, we get $(x+2x+x)+28 = 160$, which simplifies to $4x+28 = 160$.

Step4: Solve for $x$

Subtract 28 from both sides: $4x+28 - 28=160 - 28$, so $4x = 132$. Then divide both sides by 4: $x=\frac{132}{4}=33$.

Step5: Find the lengths of the other sides

The second side $b = 2x=2\times33 = 66$ feet.
The third side $c=x + 28=33+28 = 61$ feet.

Answer:

a = 33 ft
b = 66 ft
c = 61 ft