Question

The area of a square field with side 45 m is the same as the area of rectangular field with breadth 35 m. Find the length and perimeter of the rectangular field​

Answer 1

$\Large\pink {\underline {\mathfrak{~~~~~~~~~~~~~\purple {Required\:Solution}~~~~~~~~~~~~~}}}$

To find:

• Perimeter of rectangle

• Length of rectangle

Given:

• Side of square= 45 m

• Area of square = Area of rectangle

• Breadth of rectangle = 35 m

Solution:

We know:

$\bigstar \boxed {\rm{}Area~of~square=side^{2} }$

By using these Formula we can find area of square

$\dashrightarrow\sf{}Area~of~square=side^{2}$

$\dashrightarrow\sf{}Area~of~square=(45)^{2}$

$\dashrightarrow\sf{}Area~of~square = 45 \times 45$

$\dashrightarrow \underline{\boxed{\sf{}Area~of~square = 2025 {m}^{2} }}$

Now we know:

$\dashrightarrow\sf{}Area~of~square=Area~of~rectangle$

$\therefore\sf{}Area~of~rectangle = 2025 {m}^{2}$

We know:

$\bigstar \boxed {\rm{}Area~of~rectangle=length \times breadth}$

By using this formula we can find value of length of Rectangle

$\dashrightarrow\sf{}Area~of~rectangle=length \times breadth$

$\dashrightarrow\sf{}2025=length \times 35$

$\dashrightarrow\sf{} \dfrac{2025}{35} =length$

$\dashrightarrow\sf{} length = \dfrac{2025}{35}$

$\dashrightarrow\sf{} length = \dfrac{\cancel{2025}}{\cancel{35}}$

$\dashrightarrow\sf{} length = \dfrac{405}{7}$

$\dashrightarrow \underline{ \boxed{\sf{} length = 57.9m}}$

$\therefore\underline{\sf{} length \: of \: rectangle = 57.9m}$

Now Let's find perimeter:

We know:

$\bigstar \boxed {\rm{}perimeter~of~rectangle=2(length + breadth)}$

$\dashrightarrow\sf{}perimeter~of~rectangle=2(length + breadth)$

$\dashrightarrow\sf{}perimeter~of~rectangle=2(57.9+35)$

$\dashrightarrow\sf{}perimeter~of~rectangle=2(57.9)+2(35)$

$\dashrightarrow\sf{}perimeter~of~rectangle=115.8+70$

$\dashrightarrow \underline{\boxed{\sf{} perimeter~of~rectangle=185.8 \: m}}$

$\therefore \underline{\sf{} perimeter~of~rectangle=185.8 \: m}$

Answer 2

Step-by-step explanation:

$\Large\pink {\underline {\mathfrak{~~~~~~~~~~~~~\purple {Required\:Solution}~~~~~~~~~~~~~}}}$

To find:

• Perimeter of rectangle

• Length of rectangle

Given:

• Side of square= 45 m

• Area of square = Area of rectangle

• Breadth of rectangle = 35 m

Solution:

• We know:

$\bigstar \boxed {\rm{}Area~of~square=side^{2} }$

By using these Formula we can find area of square

$\dashrightarrow\sf{}Area~of~square=side^{2}$

$\dashrightarrow\sf{}Area~of~square=(45)^{2}$

$\dashrightarrow\sf{}Area~of~square = 45 \times 45$

$\dashrightarrow \underline{\boxed{\sf{}Area~of~square = 2025 {m}^{2} }}$

Now we know:

$\dashrightarrow\sf{}Area~of~square=Area~of~rectangle$

$\therefore\sf{}Area~of~rectangle = 2025 {m}^{2}$

We know:

$\bigstar \boxed {\rm{}Area~of~rectangle=length \times breadth}$

By using this formula we can find value of length of Rectangle

$\dashrightarrow\sf{}Area~of~rectangle=length \times breadth$

$\dashrightarrow\sf{}2025=length \times 35$

$\dashrightarrow\sf{} \dfrac{2025}{35} =length$

$\dashrightarrow\sf{} length = \dfrac{2025}{35}$

$\dashrightarrow\sf{} length = \dfrac{\cancel{2025}}{\cancel{35}}$

$\dashrightarrow\sf{} length = \dfrac{405}{7}$

$\dashrightarrow \underline{ \boxed{\sf{} length = 57.9m}}$

$\therefore\underline{\sf{} length \: of \: rectangle = 57.9m}$

Now Let's find perimeter:

We know:

$\bigstar \boxed {\rm{}perimeter~of~rectangle=2(length + breadth)}$

$\dashrightarrow\sf{}perimeter~of~rectangle=2(length + breadth)$

$\dashrightarrow\sf{}perimeter~of~rectangle=2(57.9+35)$

$\dashrightarrow\sf{}perimeter~of~rectangle=2(57.9)+2(35)$

$\dashrightarrow\sf{}perimeter~of~rectangle=115.8+70$

$\dashrightarrow \underline{\boxed{\sf{} perimeter~of~rectangle=185.8 \: m}}$

$\therefore \underline{\sf{} perimeter~of~rectangle=185.8 \: m}$