Question

Each side of an isosceles triangle is 13 cm and it's base is 24 cm find the area

Answer 1

☯ Given, Sides of the isosceles ∆ are 13 cm, 13 cm and 24 cm.

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$\star\:\boxed{\sf{\pink{Area_{\triangle} = \sqrt{s(s - a)(s - b)(s - c)}}}}$

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$:\implies\sf s = \dfrac{a + b + c}{2} \\\\\\:\implies\sf s = \dfrac{13 + 13 + 24}{2}\\\\\\:\implies\sf s = \cancel\dfrac{ 50}{2}\\\\\\:\implies{\underline{\boxed{\frak{\pink{s = 25\: cm}}}}}\:\bigstar$

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$\dag\;{\underline{\frak{Substituting \ values \ in \ the \ formula, }}}$⠀

$:\implies \sf:\implies Area = \sqrt{25(25-13)(25-13)(25-24)}\\ \\ \\\sf:\implies Area=\sqrt{25\times 12\times 12\times 1}\\ \\\\ \sf:\implies Area=\sqrt{5\times 5\times 12\times 12}\\ \\\\ \sf:\implies Area=5\times 12 \\\\\\:\implies{\underline{\boxed{\frak{\blue{Area_{\triangle} =60\: cm^2}}}}}\:\bigstar$

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$\therefore\:{\underline{\sf{Hence, \ area \ of \ \triangle \ is \ \bf{60 \ cm^2}.}}}$⠀⠀⠀

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