Answer:
Given that the perimeter of a triangle is 510 feet and the sides are in the ratio of 11:16:24, we can find the length of each side of the triangle using the following steps:
1. Let the sides be 11x, 16x, and 24x, where x is a common factor.
2. The sum of the sides of the triangle is equal to the perimeter, so we can write:
11x + 16x + 24x = 510 feet
Simplifying the equation, we get:
51x = 510 feet
Solving for x, we get:
x = 10 feet
3. Now, we can find the length of each side of the triangle:
Side 1 = 11x = 110 feet
Side 2 = 16x = 160 feet
Side 3 = 24x = 240 feet
4. To find the area of the triangle, we can use Heron's formula, which states that the area of a triangle with sides a, b, and c is:
Area = √(s(s-a)(s-b)(s-c))
where s is the semiperimeter of the triangle, given by:
s = (a + b + c) / 2
Substituting the values we have:
s = (110 + 160 + 240) / 2 = 255 feet
Area = √(255(255-110)(255-160)(255-240))
Area = √(255*145*95*15)
Area = 19,305 square feet
Therefore, the area of the triangle is 19,305 square feet.
Explanation: