Question

The perimeter of a triangle plot is 300m. If the length of one side is 55m, what is the area of the plot?

a. 4400 m²

b. 4150 m²

c. 2750 m²

d. 3850 m²

Answer 1

The triangle's sides are 55m, 95m, and 95m. Using Heron's formula, the area is calculated as approximately 4150 m².

b. 4150 m²

Step-by-step explanation:

The perimeter of a triangle is the sum of the lengths of its three sides. In this case, the perimeter is given as 300m, and one side is 55m. Let the other two sides be represented by 'a' and 'b'. Therefore, the equation for the perimeter is:

55 + a + b = 300

To find the values of 'a' and 'b', we can rearrange the equation:

a + b = 300 - 55 = 245

Now, the area of a triangle can be calculated using Heron's formula, which requires the lengths of all three sides. However, since we only have two sides, we need to find the length of the third side using the fact that the sum of all sides equals the perimeter. So,

a + b + 55 = 300

a + b = 245

Subtracting these two equations, we get the length of the third side:

(a + b + 55) - (a + b) = 300 - 245

55 = 55

Now that we have all three side lengths (55m, 95m, and 95m), we can use Heron's formula to find the area of the triangle. Let (s) be the semi-perimeter of the triangle, calculated as
`\((a + b + c)/(2)\).`Then, the area (A) is given by:

`\[A = √(s \cdot (s - a) \cdot (s - b) \cdot (s - c))\]`

Substituting the values, we get:

`\[s = (55 + 95 + 95)/(2) = 122.5\]`

`\[A = √(122.5 \cdot (122.5 - 55) \cdot (122.5 - 95) \cdot (122.5 - 95))\]`

After the calculation, the area is approximately 4150 m², and therefore, the correct answer is option b.