Question

5. Find the area of a triangle, two sides of why
are 15 cm and 28 cm and the perimeter
84 cm.

Ans:S=A+B+C/3
84/2
42

perimeter=A+B+C
84. =15+28+C
84. =43+C
C=84-43
C=41


Herons Formula=
$\sqrt{s(s - a)(s - b)(s - c)}$

$\sqrt{42(42 - 15)(42 - 28)(42 - 41) \} }$
$\sqrt{42(27)(1)(14)}$
$\sqrt{1134(14)}$
$\sqrt{15876}$
126cm2
​

Answer 1

$\Huge{\bf{\mathtt{\pink{AnSweR}}}}$

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$\:\:\:\:$

$\LARGE{\bf{\mathtt{\purple{GivEn}}}}$

• 1st side = 15 cm

• 2nd side = 28 cm

• perimeter = 84 cm

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$\LARGE{\bf{\mathtt{\purple{ToFinD}}}}$

• Area of the given triangle.

$\:\:\\:\:$

$\LARGE{\bf{\mathtt{\purple{ConSeDeRinG}}}}$

• Let the 3rd side be x

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$\LARGE{\bf{\mathtt{\purple{SoLuTioN}}}}$

• To find the area , we need to find the unknown side of the triangle , we already know the perimeter of triangle , so by putting values in the equation , we can find the unknown side.

• perimeter of triangle = Sum of all sides

$\:\:\:\:$

⇒ $\Large{\bf{\red{\boxed{15+28+x=84}}}}$

$\:\:\:\:$

⇒$\bf{43+x=84}$

⇒$\bf{x=84-43}$

⇒$\bf{\boxed{x=41}}$

$\:\:\:\:$

hence , 3rd side is 41 cm

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• Now , as we know all sides of triangle ,we can find the final area of the triangle.

• area of triangle by Heron's formula = $\bf{\LARGE{\sqrt{s(s - a)( s - b )( s - c )}}}$

• here s = $\bf{\LARGE{\frac{A+B+C}{3}}}$

$\:\:\:$

⇒s = $\bf{\LARGE{\frac{15+28+41}{3}}}$

⇒s = $\bf{\LARGE{\frac{84}{2}}}$

⇒s = $\bf{\LARGE{42}}$

$\:\:\:$

⇒ $\Large{\bf{\red{\sqrt{42(42-15)(42-28)(42-41)}}}}$

⇒$\Large{\bf{\sqrt{42(27)(1)(14)}}}$

⇒$\Large{\bf{\sqrt{1134(14)}}}$

⇒$\Large{\bf{\sqrt{15876}}}$

⇒$\Large{\bf{\red{area=126cm²}}}$

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Answer 2

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