Question

Herons formula area of triangle a=100b=140 c=140 solution

Answer 1

$\huge\mathtt{ANSWER:-}$

$\large\sf{\underline{\red{1500\sqrt{19}unit{}^{2}}}}$

$\huge\mathbb{\underline{\red{SOLUTION:-}}}$

$\bold{Given}\begin{cases}\sf{a=100}\\ \sf{b=140}\sf{c=140}\end{cases}$

Now heron's formula for triangle:-

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

Now:-

$\mathtt{\red{\underline{According\:to\: question:-}}}$

$\tt s=\frac{a+b+c}{2}\\ \\ \sf\longrightarrow where\:a=100\:b=140\:c=140\\ \\ \sf s=\frac{100+140+140}{2}\\ \\ \sf s=\frac{\cancel{380}}{\cancel2}\\ \\ \sf\implies s=190$

The value of s=190 Now put this in the herons formula of triangle

$\sf Area\:of\: triangle =\sqrt{s(s-a)(s-b)(s-c)}\\ \\ \sf\longrightarrow Area \sqrt{190(190-100)(190-140)(190-140)}\\ \\ \sf\longrightarrow Area=\sqrt{190×90×50×50}\\ \\ \sf\longrightarrow Area=\sqrt{10×19×3×3×10×5×10×5×10}\\ \\ \sf Area = 10×3×10×5\sqrt{19}\\ \\ \sf\longrightarrow Area =1500\sqrt{19}$

The area of triangle=$\tt 1500\sqrt{19}unit{}^{2}$

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