Question

A farmer owns a triangular plot in Guntur. He measures the sides of the plot as 4 cm, 5 cm, and 7 cm. The area of the land (in sq. cm) is:

• A. \( 2\sqrt{6} \)
• B. \( 4\sqrt{6} \)
• C. \( \sqrt{6} \)
• D. \( 8\sqrt{6} \)

Hint:

Use Heron’s formula when all three sides of a triangle are known. Remember to calculate the semi-perimeter first.

Answer 1

The Correct Option is B

Let the sides of the triangle be: \[ a = 4,\quad b = 5,\quad c = 7 \] Use Heron’s formula: \[ s = \frac{a + b + c}{2} = \frac{4 + 5 + 7}{2} = 8 \] Area: \[ \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{8(8 - 4)(8 - 5)(8 - 7)} = \sqrt{8 \cdot 4 \cdot 3 \cdot 1} = \sqrt{96} = 4\sqrt{6} \]