Question

If the area of a rhombus is 96 sq cm and one of the its diagonal is 16 cm, find other diagonal.​

Answer 1

Area of rhombus = 96 cm²

Length of one of the diagonals = 16 cm

Now, we have to find out length of other diagonal.

We know that :-

$\boxed{ \rm \large A = \dfrac{1}{2} \times d_1 \times d_2} \\ \: \\ \rm where \: A = area \: of \: rhombus \\ \rm \: d_1 and \: d_2 \: are \: diagonals$

Let length of other diagonal be x.

According to the question :-

$\rm\large \longrightarrow 96= \dfrac{1}{2} \times 16 \times x \\ \\ \large\rm \longrightarrow 96= \dfrac{1}{1} \times 8 \times x \\ \\\large \rm \longrightarrow 96= 8 \times x \\ \\\rm \large\longrightarrow \dfrac{96}{8} = x\\ \\\rm \large\longrightarrow 12 \: cm= x$

Therefore , length of other diagonal = 12 cm

Answer : 12 cm

Answer 2

QUESTION:-

If the area of a rhombus is 96 sq cm and one of the its diagonal is 16 cm, find other diagonal.

ANSWER:-

Given:-

• the area of a rhombus is 96 cm²

• one of the diagonal is 16 cm

To find:-

• find other diagonal

Required formula:-

$\begin{gathered} \boxed{ \rm \large Area\:rhombus= \dfrac{1}{2}× product\:of\:diagonals}\\\end{gathered}$

Solution:-

The area of a rhombus is 96 cm and

one of the diagonal is 16 cm

Let ,the other diagonal be ' x ' cm

According to the question:-

$\sf{:\implies \dfrac{1}{2}×16×x=96}$

$\sf{:\implies 8x=96}$

$\sf{:\implies x=\dfrac{96}{8}}$

$\sf{:\implies x=12}$

$\therefore{\underline{\sf{The\:other\:diagonal\:of\:the\:rhombus\:is\:12\:cm}}}$

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