Question

There is a rectangle of length 22 cm . Find its area if its perimeter is 75 cm.​ How explain step by step

Answer 1

Answer:

The area of the rectangle is 341 cm²

Step-by-step explanation:

Given :

• The length of the rectangle is 22 cm
• The Perimeter of the rectangle is 75 cm

To find :

the area of the rectangle

Solution :

First, we have to find the width of the rectangle.

Let 'b' be the width of the rectangle

Perimeter of the rectangle = 2(length + width)

75 cm = 2(22 + b) cm

75 = 44 + 2b

2b = 75 – 44

2b = 31

b = 31/2

b = 15.5 cm

we know that,

Area of the rectangle = length × width

Area = 22 cm × 15.5 cm

Area = 341 cm²

Therefore, the area of the rectangle is 341 cm²

Answer 2

Step-by-step explanation:

★ Concept :-

Here we use the concept of Area of Rectangle. As we see, that we are given the length and the perimeter of the rectangle. Then firstly, we will find out the breadth of the rectangle using the formula of perimeter of rectangle. After that, by applying the required values in the formula of Area of Rectangle we will get the answer.

Let's do it !!!

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★ Formula Used :-

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

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

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★ Solution :-

Given,

➼ Length of rectangle = 22cm.

➼ Perimeter of rectangle = 75cm.

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~ For the breadth of the rectangle ::

We know that,

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

⦾ By applying the values, we get :-

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

$\sf \mapsto {75\ =\ \bf 2(22\ +\ b)}$

$\sf \mapsto {75\ =\ \bf 44\ +\ 2b}$

$\sf \mapsto {2b\ =\ \bf 75\ -\ 44}$

$\sf \mapsto {2b\ =\ \bf 31}$

$\sf \mapsto {b\ =\ \bf \cancel \dfrac{31}{2}}$

$\bf \mapsto {Breadth,\ b\ =\ {\red {15.5cm.}}}$

∴ Hence, breadth of rectangle = 15.5cm.

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~ For the area of the rectangle ::

We know that,

$\sf : \implies {Area\ of\ Rectangle\ =\ \bf length \times breadth}$

⦾ By applying the values, we get :-

$\sf : \implies {Area\ of\ Rectangle\ =\ \bf length \times breadth}$

$\sf : \implies {Area\ of\ Rectangle\ =\ \bf 22cm \times 15.5cm}$

$\bf : \implies {Area\ of\ Rectangle\ =\ \bf {\orange {341cm^2.}}}$

∴ Hence, area of rectangle = 341cm².

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★ More to know :-

↬ The opposite sides are parallel and equal to each other.

↬ Each interior angle is equal to 90°.

↬ The sum of all the interior angles is equal to 360°.

↬ The diagonals bisect each other.

↬ Both the diagonals have the same length.

↬ Diagonal of rectangle = √l² + b².