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Find the area of the triangular field whose sides are 91m, 98m and 105m.

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4116

c m^{2}

c m^{2}

c m^{2}

c m^{2}

answer is A.

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Detailed Solution

https://www.vedantu.com/question-sets/44b577ec-ddf2-47e3-b3da-3f5a2782c6ee6255646389855683058.png

Given, a = 91, b = 98 and c = 105
Calculating S(semi perimeter) by using,

S = \frac{a + b + c}{2}, S = \frac{91 + 98 + 105}{2}

S = \frac{294}{2}

S=147 m.
Heron’s Formula is given as:

Area Of Triangle = \sqrt{S (S - a) (S - b) (S - c)} Area of triangle :

= \sqrt{147 (147 - 91) (147 - 98) (147 - 105)}

= \sqrt{147 \times 56 \times 49 \times 42}

\sqrt{3 \times 7 \times 7 \times 7 \times 2 \times 2 \times 2 \times 7 \times 7 \times 7 \times 3 \times 2}

= \sqrt{7 \times 7 \times 7 \times 3 \times 2 \times 2}

= 4116

c m^{2}

Therefore, the area of the triangle of given sides is

4116 m^{2}

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