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 25 feet more than the length of the shortest side. find the dimensions if the perimeter is 141 feet. what is the length of the shortest side? the length of the shortest side is 29 feet. what is the length of the second side? the length of the second side is 58 feet. what is the length of the third side? the length of the third side is

Explanation:

Step1: Identify side - length relationships

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 $(2x + 25)$ feet.

Step2: Set up the perimeter equation

The perimeter $P$ of a triangle is the sum of the lengths of its sides. So, $P=x + 2x+(2x + 25)$. Given that $P = 141$ feet, we have the equation $x+2x+(2x + 25)=141$.

Step3: Simplify the left - hand side of the equation

Combining like terms, we get $(x + 2x+2x)+25=141$, which simplifies to $5x+25 = 141$.

Step4: Solve for $x$

Subtract 25 from both sides: $5x+25−25=141 - 25$, so $5x=116$. Then divide both sides by 5: $x=\frac{116}{5}=23.2$ feet. The second - side length is $2x = 2\times23.2 = 46.4$ feet, and the third - side length is $2x + 25=46.4+25 = 71.4$ feet. But from the problem, we are given that the shortest side is 29 feet.
The second - side length: Since one side is twice the shortest side, if the shortest side $x = 29$ feet, the second - side length is $2\times29=58$ feet.
The third - side length: The third side is 25 feet more than the second side. So the third - side length is $58 + 25=83$ feet.

Answer:

The length of the shortest side is 29 feet, the length of the second side is 58 feet, and the length of the third side is 83 feet.