Question

the perimeter of rhombus is 100 CM and one of it, s diagonal is 48 CM find the other diagonal and the area of perimeter?
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Answer 1

ANSWER:-

Given:

•The perimeter of rhombus is 100cm.

•One diagonal is 48cm.

To find:

•The other diagonal & area of rhombus.

Explanation:

Perimeter of rhombus:

$= > 2 \sqrt{ {d1}^{2} + {d2}^{2} }$

So,

$= > 100 = 2 \sqrt{ {48}^{2} + {d2}^{2} } \\ \\ = > 50 = \sqrt{2304 + {d2}^{2} } \\ [squaring \: both \: sides] \\ \\ = > {50}^{2} = 2304 + {d2}^{2} \\ \\ = > 2500 = 2304 + {d2}^{2} \\ \\ = > {d2}^{2} = 2500 - 2304 \\ \\ = > {d2}^{2} = 196 \\ \\ = > d2 = \sqrt{196} \\ \\ = > d2 = 14cm$

Now,

Area of rhombus:

$= > \frac{1}{2} \times d1 \times d2 \\ \\ = > \frac{1}{2} \times 48cm \times 14cm \\ \\ = > 48cm \: \times 7cm \\ \\ = > 336 {cm}^{2}$

Thus,

The other diagonal is 14cm &

Area of rhombus is 336cm².

Thank you.

Answer 2

Answer:

ANSWER:-

Given:

•The perimeter of rhombus is 100cm.

•One diagonal is 48cm.

To find:

•The other diagonal & area of rhombus.

Explanation:

Perimeter of rhombus:

= > 2 \sqrt{ {d1}^{2} + {d2}^{2} }=>2

d1

2

+d2

2

So,

\begin{gathered} = > 100 = 2 \sqrt{ {48}^{2} + {d2}^{2} } \\ \\ = > 50 = \sqrt{2304 + {d2}^{2} } \\ [squaring \: both \: sides] \\ \\ = > {50}^{2} = 2304 + {d2}^{2} \\ \\ = > 2500 = 2304 + {d2}^{2} \\ \\ = > {d2}^{2} = 2500 - 2304 \\ \\ = > {d2}^{2} = 196 \\ \\ = > d2 = \sqrt{196} \\ \\ = > d2 = 14cm\end{gathered}=>100=2

48

2

+d2

2

=>50=

2304+d2

2

[squaringbothsides]

=>50

2

=2304+d2

2

=>2500=2304+d2

2

=>d2

2

=2500−2304

=>d2

2

=196

=>d2=

196

=>d2=14cm

Now,

Area of rhombus:

\begin{gathered} = > \frac{1}{2} \times d1 \times d2 \\ \\ = > \frac{1}{2} \times 48cm \times 14cm \\ \\ = > 48cm \: \times 7cm \\ \\ = > 336 {cm}^{2} \end{gathered}1Area of rhombus:

\begin{gathered} = > \frac{1}{2} \times d1 \times d2 \\ \\ = > \frac{1}{2} \times 48cm \times 14cm \\ \\ = > 48cm \: \times 7cm \\ \\ = > 336 {cm}^{2} \end{gathered}

=>

2

1

×d1×d2

=>

2

1

×48cm×14cm

=>48cm×7cm

=>336cm

2

Thus,

The other diagonal is 14cm &

Area of rhombus is 336cm².

Thank you2Area of rhombus:

\begin{gathered} = > \frac{1}{2} \times d1 \times d2 \\ \\ = > \frac{1}{2} \times 48cm \times 14cm \\ \\ = > 48cm \: \times 7cm \\ \\ = > 336 {cm}^{2} \end{gathered}

=>

2

1

×d1×d2

=>

2

1

×48cm×14cm

=>48cm×7cm

=>336cm

2

Thus,

The other diagonal is 14cm &

Area of rhombus is 336cm².

Thank you