AP EAMCET · Maths · Properties of Triangles
A farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as \(4 \mathrm{~cm} .5 \mathrm{~cm}\) and \(7 \mathrm{~cm}\). Then the area of land of the farmer in sq. \(\mathrm{cm}\) is
- A \(2 \sqrt{6}\)
- B \(4 \sqrt{6}\)
- C \(\sqrt{6}\)
- D \(8 \sqrt{6}\)
Answer & Solution
Correct Answer
(B) \(4 \sqrt{6}\)
Step-by-step Solution
Detailed explanation
\(a=4 \mathrm{~cm}, b=5 \mathrm{~cm}, c=7 \mathrm{~cm}\) \(\begin{aligned} & s=\frac{a+b+c}{2}=\frac{4+5+7}{2}=8 \mathrm{~cm} \\ & \text { Area of triangle }=\sqrt{s(s-a)(s-b)(s-c)} \\ & =\sqrt{8 \times 4 \times 3 \times 1} \\ & =4 \sqrt{6} \mathrm{~cm}^2\end{aligned}\)
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