Triangular Plot Area Calculation

The problem asks us to find the area of a triangular plot given its side ratios and perimeter.

Understanding Side Ratios and Perimeter

• The side ratios are given as 3:4:5. This is a key indicator of a right-angled triangle, as it forms a Pythagorean triple ($3^2 + 4^2 = 5^2$).
• The perimeter of the plot is 60 m. The perimeter is the sum of the lengths of all sides.

Calculating Actual Side Lengths

Let the sides of the triangle be $3x$, $4x$, and $5x$, where $x$ is a common multiplier.

The perimeter is the sum of these sides:

$ \text{Perimeter} = 3x + 4x + 5x $

$ \text{Perimeter} = 12x $

We are given that the perimeter is 60 m:

$ 12x = 60 \text{ m} $

Solve for $x$:

$ x = \frac{60}{12} $

$ x = 5 \text{ m} $

Now, calculate the actual lengths of the sides:

• Side 1: $3x = 3 \times 5 = 15$ m
• Side 2: $4x = 4 \times 5 = 20$ m
• Side 3: $5x = 5 \times 5 = 25$ m

Determining Triangle Type and Area

Since the sides are in the ratio 3:4:5, the triangle is a right-angled triangle. The sides 15 m and 20 m are the base and height (the two shorter sides perpendicular to each other).

The formula for the area of a right-angled triangle is:

$ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} $

Substitute the values of the base and height:

$ \text{Area} = \frac{1}{2} \times 15 \text{ m} \times 20 \text{ m} $

$ \text{Area} = \frac{1}{2} \times 300 \text{ m}^2 $

$ \text{Area} = 150 \text{ m}^2 $

Final Answer

The area of the triangular plot is 150 m².