Question

A kite has an area of 192 sq cm. If the length of one diagonal is 16 cm, find the length of the other diagonal.

Answer 1

GIVEN:-

$\large{\sf{A\: kite \:has \:an \:area\: of\: 192\:{cm}^{2}}}$

Length of one diagonal = 16 cm

To Find:-

Length of other diagonal.

SOLUTION:-

First let us know that a kite is a quadrilateral with two adjacent pairs of sides of equal length. A rhombus is a quadrilateral with all sides of equal length. So a rhombus does have two pairs of adjacent sides of equal length and is therefore a kite.

So a kite is a rhombus.

We know that the formula of area of rhombus is:-

$\large\boxed{\sf{area \: of \: rhombus \: = \frac{1}{2} \times (diagonal \: 1 \: \times \: diagonal \: 2)}}$

Let the other diagonal be x.

So,

According to the question,

$\large\Longrightarrow{\sf{192=\frac{1}{2}\times(d_1\:\times\:d_2)}}$

$\large\Longrightarrow{\sf{192=\frac{1}{2}\times(16\times\:x)}}$

$\large\Longrightarrow{\sf{192=8x}}$

$\large\Longrightarrow{\sf{\frac{192}{8}=x}}$

$\large\Longrightarrow{\sf{24=x}}$

$\large\blue\therefore\boxed{\sf{\blue{The\: other\: diagonal \:is\: 24 \:cm.}}}$

Now let's verify it:-

$\large\Longrightarrow{\sf{192=\frac{1}{2}\times(d_1\:\times\:d_2)}}$

$\large\Longrightarrow{\sf{192=\frac{1}{2}\times(16\:\times\:24)}}$

$\large\Longrightarrow{\sf{192=\frac{1}{2}\times\:384}}$

$\large\Longrightarrow{\sf{192=192}}$

$\large\therefore\boxed{\sf{LHS=RHS}}$

$\huge\pink\therefore\boxed{\sf{\pink{The\: other\: diagonal \:is\: 24 \:cm.}}}$

Answer 2

Answer:

24cm is the length of the other diagonal of a kite.

Step-by-step explanation:

Explanation:

Given, the area of a kite = 192 $cm^2$

length of one diagonal is 16cm.

A quadrilateral called a kite has two pairs of sides that are each the same length and are adjacent to one another.

So the area of a kite = $\frac{1}{2}$ ×$d_1$×$d_2$ .

Where $d_1 and d_2$ are the diagonals of the kite.

Step 1:

Therefore, area of kite = $192cm^2$ and $d_1 = 16$         [Given]

Area of kite =  $\frac{1}{2}$ ×$d_1$×$d_2$.

⇒ 192 = $\frac{1}{2}$ × (16)×$d_2$

⇒$d_2$ = $\frac{192 }{16}$× 2 = 24cm

Final answer:

Hence, the length of the other diagonal is 24 cm.

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