Question

An isosceles triangle has perimeter 18 cm and each of the equal sides is 5 cm. Find the area of the triangle

Answer 1

answer for the isosceles angle = 24

Answer 2

$\color{red}\large\underline{\underline{Question:}}$

$\textsf{An isosceles triangle has perimeter 18 cm}$ $\textsf{and each of the equal sides is 5 cm.}$ $\textsf{Find the area of the triangle .}$

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$\color{purple}\large\underline{\underline{To\:Find:}}$

• $\mathtt{The\:area\:of\:the\:triangle}$

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$\color{blue}\large\underline{\underline{Concept:}}$

$\textit{To find the area of triangle we should}$$\textit{first find the third side of the triangle}$

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$\color{green}\large\underline{\underline{Taken:}}$

• $\mathrm{Let\:the\:third\:side\:be\:x}$

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n

$\color{lime}\large\underline{\underline{Given:}}$

• $\mathtt{Perimeter = 18cm}$
• $\mathtt{Equal\:sides = 6cm}$

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$\color{magenta}\large\underline{\underline{We\:know:}}$

$\mathrm{For\:isosceles\:triangle}$

• $\mathtt{Perimeter = Sum\:of\:it's\:sides}$
• $\mathtt{Area = \dfrac{1}{2}b\sqrt{(a^{2} + \dfrac{b^{2}}{4})}}$

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$\color{orange}\large\underline{\underline{Solution:}}$

$\mathrm{The\:third\:side}$

$\textit{From the Formula:}$

$Perimeter = Sum\:of\:it's\:sides$

$\mathtt{\Rightarrow 18 = x + 5 + 5}$

$\mathtt{\Rightarrow 18 = x + 10}$

$\mathtt{\Rightarrow 18 - 10 = x}$

$\mathtt{\Rightarrow 8 = x}$

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$\mathtt{The\:area\:of\:the\:triangle}$

$\textit{From the Formula:}$

$\mathtt{Area = \dfrac{1}{2}b\sqrt{\left(a^{2} + \dfrac{b^{2}}{4}\right)}}$

$\Rightarrow Area = \dfrac{1}{2}\times 5 \times \sqrt{\left(8^{2} + \dfrac{</p><p>5^{2}}{4}\right)}$

$\Rightarrow Area = \dfrac{1}{2}\times 5 \times \sqrt{\left(64 + \dfrac{25}{4}\right)}$

$\Rightarrow Area = \dfrac{5}{2} \times \sqrt{\left(64 + \dfrac{25}{4}\right)}$

$\Rightarrow Area = \dfrac{5}{2} \times \sqrt{\left(\dfrac{256 + 25}{4}\right)}$

$\Rightarrow Area = \dfrac{5}{2} \times \sqrt{\left(\dfrac{281}{4}\right)}$

$\Rightarrow Area = \dfrac{5}{2} \times \left(\dfrac{\sqrt{281}}{2}\right)$

$\Rightarrow Area = \left(\dfrac{5\sqrt{281}}{4}\right)$

${\boxed{\therefore Area = \left(\dfrac{5\sqrt{281}}{4}\right)}}$

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