The length and breadth of a rectangle are (3x - 4y) and (2x - 3y) units resp. Find its area
(i) If the length is increased by 3y units and the breadth is increased by 2y units, what would the area of the new rectangle be?
(ii) Find the difference between the area of the two rectangles
old area = (3x-4y)(2x-3y)
new length = 3x-4y + 3
new width = 2x-3y + 3
new area = (3x-4y+3)(2x-3y+3)
for the difference subtract the two.
You would expand each one then collect like terms
To find the area of the rectangle, we multiply its length and breadth.
Given:
Length = 3x - 4y units
Breadth = 2x - 3y units
(i) If the length is increased by 3y units and the breadth is increased by 2y units, the new length and breadth would be:
New Length = (3x - 4y) + 3y
New Breadth = (2x - 3y) + 2y
To find the area of the new rectangle, we multiply the new length and new breadth:
Area of new rectangle = New Length * New Breadth
(ii) To find the difference between the area of the two rectangles, we subtract the area of the original rectangle from the area of the new rectangle:
Difference in area = Area of new rectangle - Area of original rectangle
Let's calculate these step by step:
(i) To find the area of the new rectangle:
New Length = (3x - 4y) + 3y
= 3x - y
New Breadth = (2x - 3y) + 2y
= 2x - y
Area of new rectangle = New Length * New Breadth
= (3x - y) * (2x - y)
= 6x^2 - 3xy - 2xy + y^2
= 6x^2 - 5xy + y^2
(ii) To find the difference between the area of the two rectangles:
Area of original rectangle = (3x - 4y) * (2x - 3y)
= 6x^2 -9xy -8xy + 12y^2
= 6x^2 - 17xy + 12y^2
Difference in area = Area of new rectangle - Area of original rectangle
= (6x^2 - 5xy + y^2) - (6x^2 - 17xy + 12y^2)
= 6x^2 - 5xy + y^2 - 6x^2 + 17xy - 12y^2
= -5xy + y^2 + 17xy - 12y^2
= 12xy - 11y^2
Therefore, the area of the new rectangle is 6x^2 - 5xy + y^2 units and the difference between the area of the two rectangles is 12xy - 11y^2 units.
To find the area of a rectangle, you multiply its length by its width. Let's start by finding the area of the original rectangle.
The length of the rectangle is (3x - 4y) units.
The width of the rectangle is (2x - 3y) units.
(i) To find the area of the new rectangle when the length is increased by 3y units and the width is increased by 2y units, we need to calculate the new dimensions of the rectangle.
The new length is (3x - 4y) + 3y = 3x - y units.
The new width is (2x - 3y) + 2y = 2x - y units.
To find the area of the new rectangle, we multiply the new length by the new width:
Area of the new rectangle = (3x - y) * (2x - y) square units.
(ii) To find the difference between the areas of the two rectangles, we subtract the area of the original rectangle from the area of the new rectangle:
Difference in areas = Area of the new rectangle - Area of the original rectangle.
Now, let's substitute the values and simplify the expressions:
Area of the original rectangle = (3x - 4y) * (2x - 3y) square units.
Difference in areas = (3x - y) * (2x - y) - (3x - 4y) * (2x - 3y) square units.
To further simplify the expressions, you can multiply the terms using the distributive property and combine like terms.
I hope this explanation helps you understand how to find the area of the given rectangle and the difference between the areas of the two rectangles.