If semi perimetre of a triangle is132 cm and the product of their differences between semiperimetre and the respective sides is 13200cm.Find its area.

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Solution

Given semi perimeter = S = 132
Product of the diff. between semi perimeter and sides = 13200
(s - a) (s - b) (s - c) = 13200
$∴$ Area using Heron's formula =
$\sqrt{s (s - a) (s - b) (s - c)}$
$= \sqrt{132 \times 13200}$
$= \sqrt{132 \times 132 \times 100}$
$= \sqrt{132^{2} \times 10^{2}}$
$= 132 \times 10 = 1320 c m^{2}$

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If semi perimetre of a triangle is132 cm and the product of their differences between semiperimetre and the respective sides is 13200cm.Find its area.

Given semi perimeter = S = 132 Product of the diff. between semi perimeter and sides = 13200 (s - a) (s - b) (s - c) = 13200 ∴ Area using Heron's formula = √s(s−a)(s−b)(s−c) =√132×13200 =√132×132×100 =√1322×102 =132×10=1320 cm2