Find the area of a square with side 5x2y

Mathematics is a subject with vast scope. It is divided into various branches as arithmetic, algebra, geometry, statistics, etc. Mathematics becomes part of education from the very beginning. Initially, students are introduced to basic mathematics and later to its various branches as the level is upgraded.Algebra is also one of the branches of mathematics that are introduced at the elementary level. The study of algebra involves the simplification of known and unknown values by algebraic operations. The known values of the equations are represented by real numbers and the unknown values are expressed by letters.What are algebraic expressions?Algebraic expressions are the combination of variables, coefficient of variables, constants, exponent values, and algebraic operations like addition, subtraction, multiplication, and division. Each combination of coefficient, variable and constant is known as the term. And, on the basis of these number of terms algebraic expressions are divided into three types.Types of Algebraic expressionsExpressionsTermsExampleMonomial expression1 2x3Binomial expression25y-3Polynomial expressionmore than 22x24xy-4Find the area of a square with a side of 5x2y.SolutionLength of one side of square 5x2yAs we know all sides of a square are equal to each other. (5x2y)2 25x4y2Hence, the area of the square is 25x4y2.Sample QuestionsQuestion 1. If the value of 5x-2y is equal to 7 and xy is equal to 2. What is the value of (5x2y)2.SolutionGiven,5x-2y7...........(I)xy2.................(ii)Squaring equation (I) on both sides , (5x-2y)2(7)2 25x24y2-20xy49Substituting the value of equation (ii) 25x24y24920xy 25x24y24920 2 25x24y289..............(iii)Now, finding the value of (5x2y)2 (5x2y)2 (5x)2(2y)22(5x)(2y) 25x24y220xy 8920 2 (5x2y)2 129Hence, the value of (5x2y)2 is 129.Question 2. Find the perimeter of a square with side 2x.Solutionlength of one side of square(l) 2xperimeter of square (P) 4l 4(2x) 8xHence, the perimeter of the square is 8x.Question 3. If a rectangle has area x212xy-27y2 and length x9y, find breadth of the rectangle.SolutionLength of rectangle(l) x9yArea of rectangle (A) x212xy-27y2Now,breadth Area length Texfracx212xy-27y2x9yTex Texfracx29xy3xy27y2x9yTex Texfracx(x9y)3y(x9y)x9yTex Texfrac(x9y)(x3y)x9yTex x3yHence, the breadth of the rectangle is x3y.Question 4. Find the length of a rectangle having breadth x3 and area of x27x12. SolutionArea of rectangle(A) x27x12Breadth (b) x3Now, Area lengthX breadthlength Texfracx27x12x3Tex Texfracx24x3x12x3Tex Texfracx(x4)3(x4)x3Tex Texfrac(x4)(x3)x3Tex x 4Hence, the length of the rectangle is x 4.

Find the area of a square with side 5x²y

Last Updated : 29 Oct, 2021

Mathematics is a subject with vast scope. It is divided into various branches as arithmetic, algebra, geometry, statistics, etc. Mathematics becomes part of education from the very beginning. Initially, students are introduced to basic mathematics and later to its various branches as the level is upgraded.

Algebra is also one of the branches of mathematics that are introduced at the elementary level. The study of algebra involves the simplification of known and unknown values by algebraic operations. The known values of the equations are represented by real numbers and the unknown values are expressed by letters.

What are algebraic expressions?

Algebraic expressions are the combination of variables, coefficient of variables, constants, exponent values, and algebraic operations like addition, subtraction, multiplication, and division. Each combination of coefficient, variable and constant is known as the term. And, on the basis of these number of terms algebraic expressions are divided into three types.

Types of Algebraic expressions

Expressions	Terms	Example
Monomial expression	1	2x³
Binomial expression	2	5y-3
Polynomial expression	more than 2	2x²+4xy-4

Find the area of a square with a side of 5x²y.

Solution:

Length of one side of square = 5x²y

As we know all sides of a square are equal to each other.

= (5x²y)²

= 25x⁴y²

Hence, the area of the square is 25x⁴y².

Sample Questions

Question 1. If the value of 5x-2y is equal to 7 and xy is equal to 2. What is the value of (5x+2y)².

Solution:

Given,

5x-2y=7………..(I)

xy=2……………..(ii)

Squaring equation (I) on both sides ,

=>(5x-2y)²=(7)²

=>25x²+4y²-20xy=49

Substituting the value of equation (ii)

=>25x²+4y²=49+20xy

=>25x²+4y²=49+20×2

=>25x²+4y²=89…………..(iii)

Now, finding the value of (5x+2y)²

=>(5x+2y)²= (5x)²+(2y)²+2(5x)(2y)

= 25x²+4y²+20xy

= 89+20×2

=>(5x+2y)² =129

Hence, the value of (5x+2y)²is 129.

Question 2. Find the perimeter of a square with side 2x.

Solution:

length of one side of square(l) = 2x

perimeter of square (P) = 4l

= 4(2x)

= 8x

Hence, the perimeter of the square is 8x.

Question 3. If a rectangle has area x²+12xy-27y² and length x+9y, find breadth of the rectangle.

Solution:

Length of rectangle(l) = x+9y

Area of rectangle (A)= x²+12xy-27y²

Now,

breadth = Area/ length

= $\frac{x^2+12xy-27y^2}{x+9y}$

= $\frac{x^2+9xy+3xy+27y^2}{x+9y}$

= $\frac{x(x+9y)+3y(x+9y)}{x+9y}$

= $\frac{(x+9y)(x+3y)}{x+9y}$

= x+3y

Hence, the breadth of the rectangle is x+3y.

Question 4. Find the length of a rectangle having breadth x+3 and area of x²+7x+12.

Solution:

Area of rectangle(A) = x²+7x+12

Breadth (b) = x+3

Now,

Area = lengthX breadth

length = $\frac{x^2+7x+12}{x+3}$

= $\frac{x^2+4x+3x+12}{x+3}$

= $\frac{x(x+4)+3(x+4)}{x+3}$

= $\frac{(x+4)(x+3)}{x+3}$

= x + 4

Hence, the length of the rectangle is x + 4.