Question

The perimeter of a triangle is 108 m. The difference of three side of a triangle from half its perimeter is 16 m, 18 m, 8m , respectively. Find the area of the triangle

Answer 1

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Answer 2

$\bf \large \it{Hey \: User!!!}$

$\sf \: given \: the \: perimeter \: of \: the \\ \sf triangle = 108cm \\ \\ \sf therefore \: its \: semi \: perimeter \: \\ \sf \: is = \frac{108}{2} = 54cm \\ \\ \sf \: according \: to \: the \: question , \: the \\ \sf \: difference \: of \: three \: side \: of the \: \\ \sf \: triangle \: from \: its \: semi \: perimeter \\ \sf \: is \: 16 m, 18 m \: and \: 8m \\ \\ \sf \: let \: the \: three \: sides \: of \: the \: triangle \\ \sf \: be \: a, b \: and \: c. \\ \\ \sf \: therefore : - \\ \\ \sf > > s - a = 16 \\ \sf > > s - b = 18 \\ \sf > > s - c = 8 \\ \\ \sf \: area \: of \: the \: triangle \: by \: herons \: \\ \sf \: formula \small = \sqrt{s(s - a)(s - b)(s - c)} \\ \sf \small = \sqrt{54 \times 16 \times 18 \times 8} \\ \sf \small = \sqrt{124416} \\ \sf \small = 2 \times 2 \times 2 \times 2 \times 3 \times 3 \sqrt{2 \times 3} \\ \sf \small = \boxed{{144 \sqrt{6} cm}^{2} } \: final \: answer$

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