Find the parameter of the rectangle with the width x and the length (x + 3)

Algebra in mathematics is a branch that studies integers and symbols. It has also some derivated formulas for the manipulation of these symbols or unknown values. In algebra, equations are related to terms, variables, constants, factors, and coefficients.

The given article discusses algebraic expressions along with their components and types. It also involves some mathematical problems of arithmetic including algebra in it. Such as measurement of area and perimeter of squares and rectangles.

What are algebraic expressions?

Expressions are made up of variables, constants, and coefficients along with algebraic operations (addition, subtraction, multiplication, etc). 

Components of algebraic expression

• Coefficient: They are the integers associated with variables.
• Variable: They are the unknown values represented by alphabetical letters.
• Constants: They are the integers or known values of the expression.

Types of algebraic expressions

On the basis of the number of terms, algebraic expressions are divided into three.

• Monomial expression: Algebraic expression that has only one term is monomial expression. For example: 5x,2xy,etc.
• Binomial expression: Algebraic expression that has two terms is binomial expression. For example: 2x+6, 5y-7, etc.
• Polynomial expression: Algebraic expression that has multiple terms more than two is polynomial expression. For example: xy+yz+zx,etc.

Find the parameter of the rectangle with the width x and the length (x + 3)

The perimeter formula for rectangle = 2(l+w)

given,

length of rectangle(l) = x + 3

width of rectangle(w) = x

Now, 

Perimeter of rectangle(P) = 2(l+w)

                                        = 2(x+3+x)

                                        = 2(2x+3)

                                        = 4x + 6

Hence, the perimeter of the rectangle is 4x+6.

Sample Questions

Question 1. The length and breadth of a rectangle are 5x+3 And 2x-6 respectively. Find perimeter.

Answer:

Given, 

length of rectangle(l) = 5x + 3

breadth of rectangle(b) = 2x – 6

Now, 

Perimeter of rectangle(P) = 2(l+b)

                                       = 2(5x+3+2x-6)

                                       = 2(7x-3)

                                      = 14x-6

Question 2. A rectangle with length 4x+3 and width x+5 is given. Find its perimeter.

Answer:

Given,

length of rectangle(l) = 4x+3

breadth of rectangle(b) = x+5

Now,

perimeter of rectangle(P) = 2(l+b)

                                        = 2(4x+3+x+5)

                                        = 2(5x+8)

                                        = 10x+16

Question 3. The length and breadth of a rectangle are x+4 And x+5. Find its area.

Answer:

Given,

length of rectangle(l) = x+4

breadth of rectangle(b) = x+5

Now,

Area of rectangle(A) = l × b

                                = (x+4) (x+5)

                                = x²+5x+4x+20

                                = x²+9x+20

Question 4. Find the perimeter of a square with a length of 3x.

Answer:

Length of  the square(l) = 3x

Now,

Perimeter of square (P) = 4l

                                     = 4(3x) = 12x