Question

The semi perimeter of a triangle is 132 cm.The product of the difference of semi perimeter and its respective side is 13200 cm3. Find the area of triangle

Answer 1

Let the side of the triangle as x
x ×x-132 =13200
x² +132x=13200
x²+132x-13200=0

Answer 2

$\underline\mathfrak{Given:-}$

• $\: \: \: \: \: \: \: Semi \: \: perimeter \: \: of \: \: triangle \: \: = \: \: {132}$

• $\: \: \: \: \: \: \: Products \: \: \: of \: \: \: the \: \: \: difference \: \: \: of \: \: \: semi \: \: \: perimeter \: \: \: and \: \: \: {it's} \: \: \: respective \: \: \: side \: \: \: are \: \: \: in \: \: \: cm \: \: \: is \: \: \: {13200{cm}}^{2}$

$\underline\mathfrak{To \: \: Find:-}$

• $\: \: \: \: \: Area \: \: of \: \: triangle?$

$\underline\mathfrak{Solutions:-}$

• $\: \: \: \: \: \: \: Let \: \: the \: \: sides \: \: be \: \: a \: cm, \: \: b \: cm, \: \: and \: \: c \: cm$

• $\: \: \: \: \: Semi \: \: perimeter \: \: {(s)} \: \: = \: \: {132} \: \: \: \: \: \: ..{(1)}$

• $\: \: \: \: \: {(s \: - \: a) \: (s \: - \: b) \: (s \: - \: c)} \: \: = \: \: {13200}\: \: \: \: \: \: ..{(2)}$

$\: \: \: \: \: \underline{Using \: \: {heroes's} \: \: formula.}$

$\: \: \: \: \: \leadsto \sqrt{s \: (s \: - \: a) \: (s \: - \: b) \: (s \: - \: c)}$

$\: \: \: \: \: \leadsto \sqrt{{132} \: \times \: {13200}} \: \: \: \: \: \: \: \: \: \: {[from \: \: {(1)} \: and \: {(2)}]}$

$\: \: \: \: \: \leadsto \sqrt{{132} \: \times \: {132} \: \times \: {100}}$

$\: \: \: \: \: \leadsto {{132} \: \times \: {10}}$

$\: \: \: \: \: \leadsto {1320} \: {cm}^{2}$

• $\: \: \: \: \: Area \: \: of \: \: triangle \: \: = \: \: {1320} \: {cm}^{2}$

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