Question

A rectangle has same area as that of a square of side 10m. if the breadth of the rectangle is 8m , find the perimeter of the rectangle.

Please explain properly​

Answer 1

Answer:

• Perimeter of the rectangle = 41 m

Step-by-step explanation:

Given that:

• A rectangle has same area as that of a square.
• Side of a square = 10 m
• Breadth of the rectangle = 8 m
• Let the length of the rectangle be x m.

To Find:

• Perimeter of the rectangle.

Formula used:

• Area of rectangle = (Length × Breadth)
• Area of square = (side × side)
• Perimeter of rectangle = 2(Length + Breadth)

According to the question:

Area of rectangle = Area of square

⇒ 8 × x = 10 × 10

⇒ 8x = 100

⇒ x = 100/8

⇒ x = 12.5

∴ Length of the rectangle = 12.5 m

Finding the perimeter of the rectangle:

• Perimeter of the rectangle = 2(Length + Breadth)
• Perimeter of the rectangle = 2(12.5 m + 8 m)
• Perimeter of the rectangle = 2 × 20.5 m
• Perimeter of the rectangle = 41 m

Answer 2

Step-by-step explanation:

★ Concept :-

✪ Here the concept of Perimeter of Rectangle has been used. As we see, that we are given a Rectangle which have same area as that of square. The side and breadth of square and rectangle is also given. Then firstly, we will find out the length of the Rectangle. After that, by applying the required values in the formula of Perimeter of Rectangle we will get the answer.

Let's do it !!!

___________________

★ Formula Used :-

$\star\;\underline{\boxed{\sf{\pink{Area\ of\ Rectangle\ =\ \bf length \times breadth.}}}}$

$\star\;\underline{\boxed{\sf{\pink{Area\ of\ Square\ =\ \bf Side \times Side.}}}}$

$\star\;\underline{\boxed{\sf{\pink{Perimeter\ of\ Rectangle\ =\ \bf 2(length\ +\ breadth).}}}}$

___________________

★ Solution :-

Given,

➽ A rectangle which have same area as that of square.

➽ Side of square = 10m.

➽ Breadth of rectangle = 8m.

• Let the length of the rectangle be "x" m.

---------------------------------------------------

~ For the length of rectangle ::

➴ We know that, by relationship,

$\sf \rightarrow {Area\ of\ Rectangle\ =\ \bf Area\ of\ Square}$

⦾ By applying the values, we get :-

$\sf \rightarrow {Area\ of\ Rectangle\ =\ \bf Area\ of\ Square}$

$\sf \rightarrow {length \times breadth\ =\ \bf side \times side}$

$\sf \rightarrow {x \times 8\ =\ \bf 10 \times 10}$

$\sf \rightarrow {8x\ =\ \bf 100}$

$\sf \rightarrow {x\ =\ \bf \cancel \dfrac{100}{8}}$

$\bf \rightarrow {Length,\ x\ =\ {\red {12.5m.}}}$

∴ Hence, length of rectangle = 12.5m.

------------------------------------------------------------

~ For the perimeter of rectangle ::

➴ We know that,

$\sf \mapsto {Perimeter\ of\ Rectangle\ =\ \bf 2(length\ +\ breadth)}$

⦾ By applying the values, we get :-

$\sf \mapsto {Perimeter\ of\ Rectangle\ =\ \bf 2(length\ +\ breadth)}$

$\sf \mapsto {Perimeter\ of\ Rectangle\ =\ \bf 2(12.5m\ +\ 8m)}$

$\sf \mapsto {Perimeter\ of\ Rectangle\ =\ \bf 2 \times 20.5m}$

$\bf \mapsto {Perimeter\ of\ Rectangle\ =\ {\orange {41m.}}}$

∴ Hence, perimeter of rectangle = 41m.