Rectangle|Area&Perimeter|Word Problem|Concept Clarification|Pair of Linear Equation in Two Variables

Rectangle|Area&Perimeter|Word Problem|Concept Clarification|Pair of Linear Equation in Two Variables
Dear Students in this Video we are gonna learn about the Rectangle and Area & Perimeter of Rectangle .Mostly Students face Problems in these type of Questions ,This Video Helps them to clear their doubts and Made word Problems Easy. Let's see this in a simple way with Pair of Linear Equation in Two Variables
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This video helps you to solve following type of Question:-
The difference between Length and Breadth of a Rectangle is 23 m. If the Perimeter is 206 m then find the area.
A rectangle is a parallelogram with four right angles. All rectangles are also parallelograms, but not all parallelograms are rectangles.
The perimeter P of a rectangle is given by the formula, P=2l+2w , where l is the length and w is the width of the rectangle.
The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.
You will often encounter word problems where two of the values in one of these formulas are given, and you are required to find the third.
Example 1:
The perimeter of a rectangular pool is 56 meters. If the length of the pool is 16 meters, then find its width.
Here the perimeter and the length of the rectangular pool are given. We have to find the width of the pool.
The perimeter P of a rectangle is given by the formula, P=2l+2w , where l is the length and w is the width of the rectangle.
Given that, the perimeter is 56 meters and the length is 16 meters. So, substitute these values into the formula.
56=2(16)+2w
Simplify.
56=32+2w
Subtract 32 from both sides.
24=2w
Divide each side by 2 .
12=w
Therefore, the width of the rectangular pool is 12 meters.
Example 2:
The area of a rectangular fence is 500 square feet. If the width of the fence is 20 feet, then find its length.
Here the area and the width of the rectangular fence are given. We have to find the length of the fence.
The area A of a rectangle is given by the formula, A=lw , where l is the length and w is the width.
Given that, the area is 500 square feet and the width is 20 feet. So, substitute these values into the formula.
500=l×20
Divide each side by 20 to isolate l .
25=l
Therefore, the length of the rectangular fence is 25 feet.
Representation of Pair Of Linear Equation In Two Variables
The pair of linear equations can be solved and represented by two methods:
Graphical Method
Algebraic Method
The general representation of a pair of linear equation in two variables say x and y is given by:
a1x + b1y + c1 = 0 ……………(1)
a2x + b2y + c2 = 0 ……………(2)
where a1, b1, c1, a2, b2, c2 are all real numbers and a12 + b12 ≠ 0, a22+ b22 ≠ 0.
If the pair of linear equations are given in the form of a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0, then three conditions arises here:
If the pair of linear equations is consistent, then: a1/a2 ≠ b1/b2
If the pair of linear equations is inconsistent, then: a1/a2 = b1/b2 ≠ c1/c2
If the pair of linear equations is dependent and consistent, then: a1/a2 = b1/b2 = c1/c2
For example, 2x-y = -1 and 3x + 2y = 9 are pair of linear equations with variables x and y. In the below diagram you can see we have found the solutions for both equations by putting the value of x to get the value of y.
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