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Mathematics

The area of the triangle whose three sides are 13 cm, 14 cm and 15 cm, is :

  1. 72 cm2

  2. 84 cm2

  3. 92 cm2

  4. 96 cm2

Mensuration

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Answer

Let a = 13 cm, b = 14 cm and c = 15 cm.

s = a+b+c2\dfrac{a + b + c}{2}

= 13+14+152\dfrac{13 + 14 + 15}{2}

= 422\dfrac{42}{2} = 21.

By formula,

Area of triangle = s(s−a)(s−b)(s−c)\sqrt{s(s - a)(s - b)(s - c)}

=21(21−13)×(21−14)×(21−15)=21×(8)×(7)×(6)=7056=84 cm2.= \sqrt{21(21 - 13) \times (21 - 14) \times (21 - 15)} \\[1em] = \sqrt{21 \times (8) \times (7) \times (6)} \\[1em] = \sqrt{7056} \\[1em] = 84 \text{ cm}^2.

Hence, option 2 is the correct option.

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