Question

Area of rectangle and area of square are equal. Perimeter of square is 68 cm. Breadth of rectangle is 5 cm. What is the perimter of rectangle?

Answer 1

Step-by-step explanation:

GiveN :-

• Area of the rectangle and area of square are equal.
• Perimeter of the square is 68 cm.
• Breadth of the rectangle is 5 cm.

To FinD :-

• The perimeter of the rectangle.

SolutioN :-

As per the information, we know that the area of the rectangle and area of the square are equal. And, we're also given that the perimeter of the square is 68 cm and the breadth of the rectangle is 5 cm. And we are asked to find out the perimeter of the rectangle.

Since, we know that the side of the square is not given. So firstly, we will find out the side of the square through which we're able to find out the area of the square that is equal to the area of rectangle. And after that, we will find out the length of the rectangle. And at last, we will find out our final solution that is perimeter of the rectangle. Let's do it !

$\rule{300}{2}$

SidE :-

• Perimeter of square = 4 × side
• 68 = 4 × side
• 68/4 = side
• 17 = side
• side = 17 cm

Hence, the required side of the square is 17 cm. Now, we'll find out the area of the square.

$\rule{300}{2}$

$\sf \red \bigstar {\underline{Finding\ area\ of\ the\ square:-}}$

$\sf : \implies {Area\ of\ square\ =\ (side)^2} \\ \\ \sf : \implies {(17\ cm)^2} \\ \\ \sf : \implies {17\ cm \times 17\ cm} \\ \\ : \implies {\underline{\boxed{\pink{\frak{289\ cm^2}}}}}$

Hence, the area of the square is 289 cm². Since, we know that the area of square and area of rectangle are equal. Hence, the area of rectangle is 289 cm². So now, we'll find out the length of the rectangle.

$\rule{300}{2}$

$\sf \red \bigstar {\underline{Finding\ length\ of\ the\ rectangle:-}}$

$\sf : \implies {Area\ of\ rectangle\ =\ l \times b} \\ \\ \sf : \implies {289\ =\ l \times 5} \\ \\ \sf : \implies {\dfrac{\cancel{289}}{\cancel 5}\ =\ l} \\ \\ \sf : \implies {57.8\ =\ l} \\ \\ : \implies {\underline{\boxed{\pink{\frak{l\ =\ 57.8\ cm}}}}}$

Hence, the required length of the rectangle is 57.8 cm. Now we have both length and breadth of the rectangle. So finally, we will find out the perimeter of the rectangle.

$\rule{300}{2}$

$\sf \red \bigstar {\underline{Finding\ perimeter\ of\ the\ rectangle:-}}$

$\sf \dashrightarrow {Perimeter\ of\ rectangle\ =\ 2(l\ +\ b)} \\ \\ \sf \dashrightarrow {2(57.8\ +\ 5)} \\ \\ \sf \dashrightarrow {2 \times 62.8} \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{125.6\ cm}}}}_{\scriptsize\blue {\sf{Perimeter\ of\ rectangle}}}}$

Hence, the required perimeter of the rectangle is 125.6 cm.

K N O W M O R E :-

Q. Area of rectangle and area of square are equal. Perimeter of square is 64 cm. Breadth of rectangle is 4 cm. What is the perimter of rectangle?

https://brainly.in/question/38274673.

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Answer 2

Step-by-step explanation:

Step-by-step explanation:

GiveN :-

Area of the rectangle and area of square are equal.

Perimeter of the square is 68 cm.

Breadth of the rectangle is 5 cm.

To FinD :-

The perimeter of the rectangle.

SolutioN :-

As per the information, we know that the area of the rectangle and area of the square are equal. And, we're also given that the perimeter of the square is 68 cm and the breadth of the rectangle is 5 cm. And we are asked to find out the perimeter of the rectangle.

Since, we know that the side of the square is not given. So firstly, we will find out the side of the square through which we're able to find out the area of the square that is equal to the area of rectangle. And after that, we will find out the length of the rectangle. And at last, we will find out our final solution that is perimeter of the rectangle. Let's do it !

$\rule{300}{2}$

SidE :-

Perimeter of square = 4 × side

68 = 4 × side

68/4 = side

17 = side

side = 17 cm

Hence, the required side of the square is 17 cm. Now, we'll find out the area of the square.

$\rule{300}{2}$

$\sf \red \bigstar {\underline{Finding\ area\ of\ the\ square:-}}$

$\sf : \implies {Area\ of\ square\ =\ (side)^2} \\ \\ \sf : \implies {(17\ cm)^2} \\ \\ \sf : \implies {17\ cm \times 17\ cm} \\ \\ : \implies {\underline{\boxed{\pink{\frak{289\ cm^2}}}}}$

Hence, the area of the square is 289 cm². Since, we know that the area of square and area of rectangle are equal. Hence, the area of rectangle is 289 cm². So now, we'll find out the length of the rectangle.

$\rule{300}{2}$

$\sf \red \bigstar {\underline{Finding\ length\ of\ the\ rectangle:-}}$

$\sf : \implies {Area\ of\ rectangle\ =\ l \times b} \\ \\ \sf : \implies {289\ =\ l \times 5} \\ \\ \sf : \implies {\dfrac{\cancel{289}}{\cancel 5}\ =\ l} \\ \\ \sf : \implies {57.8\ =\ l} \\ \\ : \implies {\underline{\boxed{\pink{\frak{l\ =\ 57.8\ cm}}}}}$

Hence, the required length of the rectangle is 57.8 cm. Now we have both length and breadth of the rectangle. So finally, we will find out the perimeter of the rectangle.

$\rule{300}{2}$

$\sf \red \bigstar {\underline{Finding\ perimeter\ of\ the\ rectangle:-}}$

$\sf \dashrightarrow {Perimeter\ of\ rectangle\ =\ 2(l\ +\ b)} \\ \\ \sf \dashrightarrow {2(57.8\ +\ 5)} \\ \\ \sf \dashrightarrow {2 \times 62.8} \\ \\ \dashrightarrow {\underbrace{\boxed{\pink{\frak{125.6\ cm}}}}_{\scriptsize\blue {\sf{Perimeter\ of\ rectangle}}}}$

Hence, the required perimeter of the rectangle is 125.6 cm.

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