Question

A triangle and a parallelogram have the same base and the same area. If the sides of
the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base
28 cm, find the height of the parallelogram.​

Answer 1

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$\huge{\underline{\underline{\sf{\blue{SOLUTION:-}}}}}$⠀

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$\sf{\underline{\pink{Answer-}}}$⠀

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• the height of the parallelogram is 12 cm.

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$\sf{\underline{\pink{Given-}}}$

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• Sides of the triangle = 26cm , 28cm and 30cm

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• The parrellelogram stand on the base = 28cm

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$\sf{\underline{\pink{Find-}}}$

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• find the height of the parallelogram.

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

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• Let the height of the parallelogram be h

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• Area of parallelogram = Area of triangle

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$</h2><h2>\sf{\underline\green{Formula\:Used\:Here-}}$

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$⠀\bigstar\:\:\boxed{\sf{\red{Heron's \: formula}}}$

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$</h2><h2>\sf{\underline{\pink{Putting\:the\:values:-}}} </h2><p></p><h2>$

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$\sf\longrightarrow Perimeter \: of \: triangle = (26 + 28 + 30) cm = 84 cm$

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$\sf\longrightarrow2s = 84 cm$

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$\sf\longrightarrow S = 42 cm$

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$</h2><h2>\sf{\underline{\green{Heron's \: formula : - }}} </h2><p></p><h2>$

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$\sf\longrightarrow Area \: of \: triangle = \sqrt{s(s - a)(s - b)(s - c)}$

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$\sf\longrightarrow( \sqrt{42(42 - 26)(42 - 28)(42 - 30 )} ^{cm2}$

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$\sf\longrightarrow( \sqrt{42(16)(14)(12)}^{cm2} = 336 {cm}^{2}$

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$\sf{\underline{\blue{Now-}}}$

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$\sf\longrightarrow Let \: the \: height \: of \: the \: parallelogram \: be \: h</p><p> \:$

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$\sf\longrightarrow Area \: of \: parallelogram = Area \: of \: triangle$

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$\sf\longrightarrow h \times 28 cm = 336 {cm}^{2} </p><p></p><p>$

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$\sf\longrightarrow h = 12 cm$

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• Therefore, the height of the parallelogram is 12 cm.

Answer 2

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(The height of the parallelogram is 12 cm.)

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