Question

if the area of square field is 7200 sq.m. then the length of it's diagonal (in mts) is​

Answer 1

Answer:-

The Length of the diagonal is 120m.

Explanation:-

Given:-

• Area of a square = 7200 sq. cm.

To Find:-

• The Length of its one of the Diagonal.

Formulas Used:-

In A Square,

1.

$\\ \large\orange{ \longrightarrow \boxed{ \pink{ \bf side {}^{2} = area.}}}$

2.

$\\ \large\orange{ \longrightarrow \boxed{ \pink{ \bf diagonal = \sqrt{2} \times side.}}}$

Now Here,

• Area = 7200 cm².

• Side = ??.

• Diagonal = ?? [To Find].

So,

By Using Formula (1):-

$\\ \bf\mapsto side {}^{2} = area.$

$\\ \tt\mapsto side {}^{2} = 7200 \: m {}^{2}$

$\\ \large \bf\mapsto side = \sqrt{7200} \: m .$

So we get the side of the square = $\bf\sqrt{7200}\:m.$

Now By Using Formula (2) we get:-

$\\ \bf\mapsto diagonal = \sqrt{2} \times side.$

$\\ \tt\mapsto diagonal = \sqrt{2} \times \sqrt{7200} \: m.$

$\\ \tt\mapsto diagonal = \sqrt{2 \times 7200} \: m.$

$\\ \tt\mapsto diagonal = \sqrt{14400} \:m.$

$\\ \large\red{\mapsto \boxed{ \blue{ \bf diagonal =120 \: m.}}}$

Therefore The Required Length Of The Diagonal Is 120 m.

Answer 2

Given ,

The area of square is 7200 m²

We know that , the area of square is given by

$\boxed{ \tt{Area = {(a)}^{2} }}$

Where , a = side

Thus ,

(a)² = 7200

a = √(7200) m

Now , the diagonal of square is given by

$\boxed{ \tt{Diagonal \: of \: square = \sqrt{2}a }}$

Thus ,

Diagonal = √2 × √(7200)

Diagonal = √(14400)

Diagonal = 120 m

Hence , the diagonal of square is 120 m