Question

The semi perimeter of a triangle is 132 cm.The product of the differences of semi perimeter and its respective sides are in cm is 13200.Find its area of the triangle ​

Answer 1

Answer:

Solution:-

Given :-  s = 132 cm and (s-a)(s-b)(s-c) = 13200 cm²

Therefore, according to the Heron's formula, 

Area of the triangle = √s(s-a)(s-b)(s-c)

Now, substituting the values, we get

Area = √132×13200

= √132×132×100

= √132×132×10×10

Area of the triangle = 132×10

Area = 1320 cm²

Answer is area=1320 cm2

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Answer 2

$\large\bf\underline{Given:-}$

• semi perimeter of triangle = 132

• product of the differences of semi perimeter and its respective sides are in cm is 13200cm.

$\large\bf\underline {To \: find:-}$

• Area of triangle.

$\huge\bf\underline{Solution:-}$

Let the sides be a cm , b cm and c cm.

• semi perimeter (s) = 132cm .........(i)

• (s - a)(s - b)(s - c) = 13200cm......(ii)

$\bf \underline{By\: heron's\: formula\:area \: of \: triangle : - }$

$\underline{ \boxed{ \mid \bf \: \sqrt{s(s - a)(s - b)(s - c)} \: \: \: \: \mid }}$

$: \implies \rm \: \sqrt{132 \times 13200} c {m}^{2}\:\: [from\:(i)\:and\:(ii)]\\ \\ : \implies \rm \: \sqrt{132 \times 132 \times 100} c {m}^{2} \\ \\ : \implies \rm \: 132 \times 10 \: cm {}^{2} \\ \\ : \implies \rm \: 1320c {m}^{2} \\ \\ \bf \therefore \: Area \: of \: triangle \: = 1320 {cm}^{2}$