Final answer:
To solve for the length of the base of the isosceles triangle, create an equation using the given ratio of the base to the leg and the perimeter, solve for x, and then calculate the base as 2x, which gives an answer of 18 feet.
Step-by-step explanation:
To find the length of the base of the isosceles triangle, we can use the given ratio of the base to the leg (2:3) and the perimeter of the triangle. Let's denote the base as 2x feet and each leg as 3x feet. Since the triangle is isosceles, it has two sides of equal length. The perimeter P of an isosceles triangle is the sum of the lengths of all three sides, which can be expressed as P = 2x + 2(3x) = 72 feet, where 2x is the base and 3x is each leg of the triangle.
Simplifying the equation, we have 2x + 6x = 72, which leads to 8x = 72. Dividing both sides of the equation by 8, we find x = 9. Therefore, the length of the base, which is 2x, equals 18 feet.
Using proportions, we don't need to write separate ratios for length and width as the question only involves a single dimension for each side of the triangle.