Question

The length of one diagonal of a rhombus is 16cm.Find the length of another diagonal if the side of the rhombus is 10 cm.​

Answer 1

Given :

The length of one diagonal of the rhombus is 16 cm. Side of The rhombus is 10 cm.

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To Find :

Find the length of the another Diagonal.

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Solution :

Let ABCD be the rhombus

AC = 16 cm

AB = 10 cm

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By phytgeores Theorem.

$: \implies \sf {10}^{2} = {8}^{2} + {BO}^{2}$

$: \implies \sf {BO}^{2} = 100 - 64 = 36$

$: \implies \sf \therefore bo = 6cm$

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$\red {\underline{ \sf {Diagonal \: BD = 2 × 6 = 12 cm}}}$

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$\blue{ \underline{ \sf {Area \: of \: Rhombus : }}} \\ {{\: \: \: : \implies \frac{1}{2}\sf{ \times product \: of \: diagnals}}}$

$\: \: \: : \implies\frac{1}{2} \times 16 \times 12$

$\: \: \: : \sf \implies 8 \times 12 = 92cm$

$\:$

Hence,

$\pink {\underline {\tt{Length \: of \: other \: diagonal = 12sq. cm}}}$

$\pink{ \underline{ \sf {\tt{Area \: of \: Rhombus = 92sq. cm}}}}$