Question

If the area of rhombus is 144 cm2

and one of its diagonal is 8 cm, find the length of its other

diagonal.​

Answer 1

Answer:

Area of rhombus = 144 cm square

One of its diagonal is double the other

let diagonal 1 (d1) be 'x '

(according to the question )

One of the diagonal is double than other

So,

diagonal 2(d2) = 2x

\begin{gathered}\bf area \: of \: rhombus = \frac{1}{2} \times d1 \times \: d 2 \\ \\ = 144 = \frac{1}{2} \times x \times 2x \\ \\ = 144 = \frac{ {2x}^{2} }{2} \\ \\ = 144 = {x}^{2} \\ \\ = \sqrt{144} = x \\ \\ = 12 = x\end{gathered}

areaofrhombus=

2

1

×d1×d2

=144=

2

1

×x×2x

=144=

2

2x

2

=144=x

2

=

144

=x

=12=x

diagonal 1 = x = 12 cm

diagonal 2 = 2x = 2 × 12 = 24 cm

CHECK

area of rhombus

\begin{gathered}\bf = \frac{1}{2} \times d1 \times d2 \\ \\ = \frac{1}{2} \times 12 \times 24 \\ \\ = 6 \times 24 \\ \\ = 144 {cm}^{2}\end{gathered}

=

2

1

×d1×d2

=

2

1

×12×24

=6×24

=144cm

2

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Answer 2

Question:༶•┈┈⛧┈♛

If the area of rhombus is 144 cm²,and one of its diagonal is 8 cm, find the length of its other diagonal.

Given:♬♩♪♩ ♩♪♩♬

• Area= 144cm²
• d¹= 8cm
• d²=?

Solution:☆♬○♩●♪✧♩　　

A/formula- Area of rhombus = ½×d¹×d²

then,

144 cm² = ½×8×d²

144×2×⅛ = d²

36 = d²

d² = 36cm

so, the other diagonal of rhombus is 36cm

To verify:⋇⋆✦⋆⋇　

L. H. S = R. H. S

Area of rhombus = ½×d¹×d²

144 = ½×8×36

144 = 144

Hence, Verified

Analysis:»»——⍟——««

Area is given = 144 cm² , first diagonal is also given= 8cm, so according to formula we can get other diagonal of the rhombus.

Formula to solve this question:

Area of rhombus = ½×d¹×d²

I have to say:»»————>

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