Question

Sides of triangle are 45cm,39cm,and 42cm.
Find its area.

Answer 1

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$\large{\underline{\boxed{\sf{\blue{Area\:of\:triangle=756\:cm^2}}}}}$

$\large{\underline{\underline{\mathfrak{\pink{\sf{Explanation-}}}}}}$

$\begin{lgathered}\bold{Given\:sides} \begin{cases}\sf{AB=45cm} \\ \sf{BC=39cm}\\ \sf{AC=42cm}\end{cases}\end{lgathered}$

$\orange{\boxed{\pink{\underline{\red{\mathfrak{To\:find-}}}}}}$

• Area of ∆ABC

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Semi perimeter :

$\sf{\dfrac{a+b+c}{2}}$

Heron's formula :

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

$\orange{\boxed{\pink{\underline{\red{\mathfrak{Solution-}}}}}}$

In ∆ABC,

Semi Perimeter ( S ) = $\sf{\dfrac{a+b+c}{2}}$

Here a = AB = 45cm

b = BC = 39cm

c = AC = 42 cm

$\implies$ $\sf{\dfrac{45+39+42}{2}}$

$\implies$ $\sf{\dfrac{126}{2}}$

$\implies$ $\sf{\cancel{\dfrac{126}{2}}}$

$\implies$ $\sf{63cm}$

By heron's formula :

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

$\implies$ $\sf{\sqrt{63(63 - 45)(63 - 39)(63 - 42)}}$

$\implies$ $\sf{\sqrt{63(18)(24)(21)}}$

Now, making prime factors,

$\implies$ $\sf{\sqrt{3×3×7(3×3×2)(2×2×2×3)(3×7)}}$

$\implies$ $\sf{\sqrt{571536}}$

$\implies$ 756 cm²

$\large{\underline{\boxed{\sf{\blue{Area\:of\:triangle=756\:cm^2}}}}}$

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