Question

if the area of a rhombus is
$80 {m}^{2}$
and one diagonal is 24m
then find the other diagonal​

Answer 1

Given: The area of a rhombus is 80m² and one diagonal of a rhombus is 24m.

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Exigency to find: The other diagonal of a rhombus.

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⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

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We know that, if we are given with the area of a rhombus & diagonal of a rhombus, we have the required formula, that is,

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$\sf{:\implies Area_{(rhombus)} = \dfrac{1}{2} \times d_1 \times d_2}$

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⠀⠀⠀⠀ Here d₁ is one diagonal of rhombus and d₂ is thr the other diagonal of rhombus. And here in this question we have Area of rhombus is 80m² and one diagonal of rhombus is 24m. So, by using the required formula we can find other diagonal of rhombus.

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By using the required formula, and substituting all the given values in the formula, we get:

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$\sf{:\implies 80 = \dfrac{1}{ \cancel{ \: 2 \: }} \times \cancel{24} \times d_2} \\ \\ \\ \sf{:\implies 80 = 1 \times 12 \times d_2} \\ \\ \\ \sf{:\implies 80 = 12 \times d_2} \\ \\ \\ \sf{:\implies 12 \times d_2 = 80} \\ \\ \\ \sf{:\implies d_2 = \cancel{\dfrac{80}{12}}} \\ \\ \\ \sf{:\implies \boxed{\pink{\frak{d_2 = 6.66}}}}$

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$\sf{\therefore{\underline{The \: other \: diagonal \: of \: rhombus \: is \: \textsf{\textbf{6.66m}.}}}}$

Answer 2

Answer:

Given :-

• area of a rhombus is 80m²
• 1st Diagonal = 24 m

To Find :-

Other Diagonal

Solution :-

We know that

Area of rhombus = ½ × D1 × D2

Let the other Diagonal be y

$\implies \sf \: 80 = \dfrac{1}{ \cancel2} \times \cancel {24 }\times y$

$\sf \implies 80 = 1 \times 12 \times y$

$\sf \implies \: 80 = 12y$

$\sf \implies \: y = \dfrac{80}{12}$

${ \textsf{ \textbf{ \underline{ \red{y = 6.66}}}}}$