Question

the area of a square is 16200m2. find the length of its diagonals​

Answer 1

Answer:

$\large\bold\red{180\;m}$

Step-by-step explanation:

Given,

Area of square,

$A = 16200 \: {m}^{2}$

Let the side of square be 'x' m

Therefore,

We get,

$= > {x}^{2} = 16200 \\ \\ = > x = \sqrt{16200} \\ \\ = > x = \sqrt{9 \times 9 \times 2 \times 10 \times 10} \\ \\ = > x = \sqrt{ {( \sqrt{2}) }^{2} \times {(9)}^{2} \times {(10)}^{2} } \\ \\ = > x = \sqrt{2} \times 9 \times 10 \\ \\ = > x = 90 \sqrt{2} \: m$

Therefore,

• Sides of square = 90√2 m

Now,

We know that,

• Diagonal of a square = √2x

Therefore,

We get,

$= > d = \sqrt{2} \times 90 \sqrt{2} \\ \\ = > d = 90 \times 2 \\ \\ = > d = 180 \: m$

Hence,

• Diagonal = 180 m

Answer 2

Given ,

Area of square = 16200 m²

To find :

Diagonal of square

Solution :

We know that , the area of square is given by -

$\large \star \: \: \sf\fbox{ \fbox{ \red{Area \: of \: square = { (side)}^{2}} }}$

Substitute the values , we obtain

$\sf \hookrightarrow16200 = {(side)}^{2} \\ \\ \sf \hookrightarrow side = \sqrt{16200} \\ \\\sf \hookrightarrow side = \sqrt{2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 3 \times 5 \times 5} \\ \\\sf \hookrightarrow side = 90 \sqrt{2} \: \: m$

Now , the diagonal of square is given by

$\star \: \: \large\fbox{\sf \fbox{ \pink{Diagonal \: of \: square = \sqrt{2} (side)}}}$

Again , substitute the value , we obtain

$\sf \hookrightarrow Diagonal = \sqrt{2} (90 \sqrt{2} ) \\ \\\sf \hookrightarrow Diagonal = 90 \times 2 \\ \\\sf \hookrightarrow Diagonal = 180 \: \: m$

Hence , the diagonal of square is 180 m