Question

The length and breath of a rectangular field are 15 m and 30 m respectively. if a square field has the same Perimeter as this field the area of the square field is?

Answer 1

➲Given that, The length and breath of a rectangular field are 15 m and 30 m respectively

_____________________

❒ To Find:

• a square field has the same Perimeter as this field the area of the square field is.?

Solution:

${ \underline{ \boxed{ \blue{ \sf{perimeter \: of \: rectangle = perimeter \: of \:square}}}}}$

$: \implies \sf \: perimeter \: of \: rectangle = 2(l + b) \: \: \: \: \: \\ \\ \\ : \implies \sf \: perimeter \: of \: rectangle = 2(15 + 30) \\ \\ \\ : \implies \sf \: perimeter \: of \: rectangle = 2 \times 45m \: \: \: \: \\ \\ \\ : \implies \sf \: perimeter \: of \: rectangle = 90 {m} \: \: \: \: \: \: \: \:$

$\rm \therefore \purple{ \underline{ \: perimeter \: of \: rectangle = 90 {m} \bigstar }}$

so the perimeter of square is:

✬90cm²✬

➺now let's find the side of the square to find the area.!

$: \implies \sf \: perimeter \: of \:square = 4 \times s \\ \\ \\ : \implies \sf \: 90cm = 4 \times s \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ : \implies \sf \: side = \cancel\frac{90}{4} m \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ : \implies \sf \: side = 22.5m \star \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now,area of square equals:

$: \longrightarrow \sf area = {22.5}^{2} \: \: \: \: \: \: \: \: \\ \\ : \longrightarrow \sf area = 506.25 {m}^{2}$

$\blue{ \underline{ \boxed{ \pink{ \mathfrak{ \therefore \: area\: of \: the \: square = 506.25 {m}^{2} }}}}}$

Answer 2

Answer:

Explanation:

Given :

• The length and breath of a rectangular field are 15 m and 30 m respectively.
• Perimeter of rectangular field = Perimeter of square field.

To Find :

• The area of the square field.

Solution :

We know that,

Perimeter of rectangular field = 2(l + b)

=> Perimeter = 2(15 + 30)

=> Perimeter = 2(45)

=> Perimeter = 90 m

Given that, Perimeter of rectangular field = Perimeter of square field.

=> 90 = 4 × a

=> a = 90/4

=> a = 22.5 m

Again, we know that,

Area of square field = a²

=> Area = 22.5²

=> Area = 506.25 m²

Hence :

The area of the square field is 506.25 m².