Question 14 of 42intermediate🔧 ApplyNumerical3 marks

The sides of a triangular plot are in the ratio 3:5:7; its perimeter is 300 m. Find its area.

Correct Answer

15003\sqrt{3} m²

Exercise: Exercise Set 6.2 | Q: 4 | (Page 25)
For More Understanding

Explanation

The problem requires finding the area of a triangle given the ratio of its sides and its perimeter. First, the actual side lengths are determined from the ratio and perimeter. Then, Heron's formula is applied using the semi-perimeter and the differences between the semi-perimeter and each side, as demonstrated in the textbook's examples.

Solution Steps

  1. Step 1: Let the sides be 3x, 5x, and 7x. Perimeter = 15x = 300 m, so x = 20. The sides are 60 m, 100 m, and 140 m.

  2. Step 2: Calculate the semi-perimeter, s = 300 / 2 = 150 m.

  3. Step 3: Apply Heron's formula: Area = √[s(s-a)(s-b)(s-c)] = √[150 × (150-60) × (150-100) × (150-140)]

  4. Step 4: Calculate Area = √[150×90150 \times 90 × 50×1050 \times 10] = 6750000\sqrt{6750000} = 15003\sqrt{3} m².

PreviousNext