Discussion
The sides of a triangular plot are in the ratio of 3 : 5 : 7 and its perimeter is 300 m. The area of the triangular plot will be
Answer: A
The area of the plot is \(1500\sqrt{3}\ \text{m}^{2}\).
Dividing the perimeter of 300 m in the ratio 3 : 5 : 7 (15 parts of 20 m each) gives sides of 60 m, 100 m and 140 m. The semi-perimeter is s = 150 m. By Heron's formula:
\[ \begin{aligned} A &= \sqrt{s(s - a)(s - b)(s - c)} \\ &= \sqrt{150 \times 90 \times 50 \times 10} \\ &= \sqrt{6750000} = 1500\sqrt{3}\ \text{m}^{2} \end{aligned} \]
since \(6750000 = 1500^{2} \times 3\). This is about 2,598 m2. The options with 1300 or \(\sqrt{5}\) do not come from these sides; a quick check is that the angle opposite the 140 m side is 120°, giving \(\frac{1}{2}(60)(100)\sin 120^{\circ} = 1500\sqrt{3}\).
Post your comment
Please log in or register to post a comment.
Examination Categories
- SSC Exams
- Banking Exams
- Teaching Exams
- Civil Services Exams
- Railways Exams
- Engineering Recruitment Exams
- Defence Exams
- State Government Exams
- Police Exams
- Insurance Exams
- Nursing Exams
- Other Government Exams
- NRA CET
- PG Entrance Exams
- Campus Placement
- MBA Entrance Exams
- CUET and UG Entrance
- Judiciary Exams
- Regulatory Body Exams
- Software Development