Question

Triangle ABC is isosceles with AB=AC=7.5cm and BC=9cm.The height from A to BC, AD is 6cm.Find
the area of triangle ABC. What will be the height from C to AB?

Answer 1

Given:-

⠀

• ABC is an isosceles triangle.

• AB = AC = 7.5 cm

• BC = 9 cm

• The height from A to BC, AD is 6cm

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To find:-

⠀

• Find the area of triangle ABC

• Find the height from C to AB

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Solution:-

⠀

In ∆ABC ,

• Base, BC = 9 cm and

• Height, AD = 6 cm

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As we know that,

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$\boxed{\bf{\pink{Area\:of\:triangle=\dfrac{1}{2}×base×height}}}$

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$\sf{:\implies Area\:of\:the\:triangle=\dfrac{1}{2}×BC×AD}$

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$\sf{:\implies Area\:of\:the\:triangle=\dfrac{1}{2}×9×6\:cm^{2}}$

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$\sf{:\implies Area\:of\:the\:triangle=3×9\:cm^{2}}$

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$\sf{:\implies Area\:of\:the\:triangle=27\:cm^{2}}$

⠀⠀

$\therefore{\underline{\sf{Area\:of\:the\:triangle\:is\:27\:cm^{2}}}}$

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Now,

Let , CE will be ' h' cm

we also know that , base of triangle ,AB = 7.5 cm

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$\sf{:\implies Area\:of\:the\:triangle=\dfrac{1}{2}×AB×CE}$

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$\sf{:\implies \dfrac{1}{2}×AB×CE=27\:cm}$

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$\sf{:\implies \dfrac{1}{2}×7.5×h=27\:cm}$

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$\sf{:\implies h=27×2×\dfrac{1}{7.5}\:cm}$

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$\sf{:\implies h=\dfrac{9×2×2}{5}\:cm}$

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$\sf{:\implies h=\dfrac{36}{5}\:cm}$

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$\boxed{\bf{\purple{:\implies h=7.2\:cm}}}$

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$\therefore{\underline{\sf{The\:height\:from\:\: to\:AB\:is\:7.2\:cm}}}$

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