Question

a rectangle has sides of length x cm and y cm. If the perimeter of the rectangle is 22cm and the area of the rectangle is 24 cm2, use algebra to find the dimensions of the rectangle

Answer 1

Solution

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• length of rectangle is x cm
• breadth of rectangle is y cm

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As we know,

⠀⠀⠀✧ Perimeter of rectangle = 2(l + b)

But it is given that, perimeter of the rectangle is 22cm. Therefore,

⇒ 2(x + y) = 22

⇒ x + y = 11⠀⠀⠀... [1]

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Similarly,

⠀⠀⠀✧ Area of rectangle = l × b

But it is given that, area of rectangle is 24 cm². Therefore,

⇒ x × y = 24

⇒ x = 24/y

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Putting the value of x in eq[1]

➛ 24/y + y = 11

➛ y² + 24 = 11y

➛ y² - 11y + 24 = 0

➛ y² - 8y - 3y + 24 = 0

➛ y(y - 8) - 3(y - 8) = 0

➛ (y - 8) (y - 3) = 0

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We get,

• y = 8
• y = 3

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Now, there's a situation where we get two values of y. Therefore, we will get two values of x as well.

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Case I

• y = 8

➛ x + 8 = 11

➛ x = 11 - 8

➛ x = 3

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Case II

• y = 3

➛ x + 3 = 11

➛ x = 11 - 3

➛ x = 8

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Hence,

• Required values are

1. x = 3 and y = 8
2. x = 8 and y = 3

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Answer 2

Answer:

Required dimension is 8 cm × 3 cm.

Step-by-step explanation:

Given, sides of rectangle are x cm and y cm.

It is also given, perimeter = 22 cm and area = 24 cm²

So, according to question,

$2 \times (x + y) = 22 \\ x + y = 11 \\ x = 11 - y$

and

$xy = 24 \\ (11 - y) \times y = 24 \\ {y}^{2} - 11y - 24 = 0 \\ {y}^{2} - 8y - 3y - 24 = 0 \\ y(y - 8) - 3(y - 8) = 0 \\ (y - 8)(y - 3) = 0 \\ y = 8 \: or \: 3$

So,

$x = 11 - 8 = 3 \\ or \: 11 - 3 = 8$

Therefore, required dimension is 8 cm × 3 cm.

This is a problem of rectangle.

Rectangle related more information :

A rectangle is a type of quadrilateral whose parallel sides are equal to each other and all four vertices are at 90 degrees. Therefore, it is also called an equilateral quadrilateral.

Since opposite sides of a rectangle are equal and parallel, it can also be called a parallelogram.

Rectangle shape:

A rectangle is a two-dimensional flat shape. In the XY plane, we can simply represent a rectangle, where the branches of the x-axis and y-axis represent the length and width of the rectangle, respectively.

Rectangular objects

The most common rectangular everyday things or objects we see are TV, computer screen, laptop, mobile phones, processor, bulletin boards, table, book, TV screen, mobile phone, wall, magazine, tennis court, etc.

The properties of a rectangle are given below:

1. It has four sides and four vertices
2. The angle of each vertex is 90 degrees
3. Opposite sides are equal and parallel
4. Diagonals bisect each other
5. The circumference is equal to twice the sum of its length and width
6. The area is equal to the product of its length and width
7. It is a parallelogram with four right angles.
8. The sum of all interior angles is 360 degrees

Rectangle related two more questions:

https://brainly.in/question/22537731

https://brainly.in/question/34004368

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