Question

area of a rhombus is 48cmsquare and one diagonal is 8cm find the other diagonal​

Answer 1

Answer:

$\large{\boxed{\mathfrak\green{Solution..}}}$

● Given:-

☆ Area of a rhombus is 48cm^2.

☆ One diagonal is 8cm.

● To find:-

☆ Other diagonal.

● Solution:-

We know that,

Area of a rhombus= (1/2 × one diagonal × other diagonal)

or, 48 = (1/2 × 8 × other diagonal)

or, 48 = (4 × other diagonal)

or, Other diagonal = 48/4

So, Other diagonal = 12 cm

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Answer 2

$\mathfrak{\huge{\underline{Solution:}}}$

Let ABCD be a Rhombus in which AC(d1) and BD(d2) are diagonals.

$\textbf{\huge{\underline{Given\:}}}$

$\rm \: Area = 48 {cm}^{2}$

$\rm \: Diagonal(d_{1}) = 8cm$

To Find the other Diagonal :

$\textbf{\underline{\underline{Formula\:Applied:}}}$

$\rm \:Area = \sf \: \dfrac{1}{2} \times d_{1} \times d_{2}$

$\hookrightarrow \: \rm \: 48 {cm}^{2} = \dfrac{1}{ \cancel2} \times \cancel8 \times d_{2}$

$\hookrightarrow \rm \: 48 {cm}^{2} = 4d_{2}$

$\hookrightarrow \rm \: d_{2} = \cancel\dfrac{48}{4}$

$\hookrightarrow \rm \: d_{2} = 12cm$

Hence,The other diagonal is 12 cm

$\mathfrak{\huge{\underline{Verification:}}}$

$\textbf{\huge{\underline{Given\:}}}$

$\rm \: Area = 48 {cm}^{2}$

$\rm \: One \: Diagonal = 8cm$

$\rm \: Other \: Diagonal = 12cm$

$\hookrightarrow \rm \: Area = \dfrac{1}{ \cancel2} \times 8 \times \cancel 12$

Hence,Verified!!

$\hookrightarrow \: \rm 48 {cm}^{2} = 48 {cm}^{2}$