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Heron's Formula · Class 9 · CBSE Mathematics

Find the area of a triangle with side lengths 13text{ cm}, 14text{ cm}, and 15text{ cm}.

Practice question from Heron's Formula (Class 9 · CBSE Mathematics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-526664

Find the area of a triangle with side lengths 13 cm13\text{ cm}, 14 cm14\text{ cm}, and 15 cm15\text{ cm}.

  1. A.84 cm^2Correct answer
  2. B.90 cm^2
  3. C.65 cm^2
  4. D.42 cm^2

Solution

Semi-perimeter s=13+14+152=21 cms = \frac{13 + 14 + 15}{2} = 21\text{ cm}. Using Heron's formula, Area = 21(21−13)(21−14)(21−15)=21×8×7×6=(3×7)×(4×2)×7×(2×3)=72×32×42=7×3×4=84 cm2\sqrt{21(21-13)(21-14)(21-15)} = \sqrt{21 \times 8 \times 7 \times 6} = \sqrt{(3 \times 7) \times (4 \times 2) \times 7 \times (2 \times 3)} = \sqrt{7^2 \times 3^2 \times 4^2} = 7 \times 3 \times 4 = 84\text{ cm}^2.

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