Respuesta :
Answer:
200%
Step-by-step explanation:
Length and breadth is in the ratio 2:3
Then, let length = 2x and breadth = 3x
Area of rectangle = l×b = 2x×3x = 6[tex]x^{2}[/tex]
Now if breadth is increased by 50% ,
our new breadth will be = 3x + 50%(3x)
= 4.5x
And length is increased by same number of units, length = 2x+ 2x = 4x
New area = l×b = 4.5x × 4x
= 18[tex]x^{2}[/tex]
Percentage change in area = [tex]\frac{New area - old area}{old area}[/tex]×1000
= [tex]\frac{18x^{2}-6x^{2} }{6x^{2} }[/tex]×100
= 200%
Answer:
The area of rectangle is increased by 200%
Step-by-step explanation:
Given the ratio of the width to the length of a rectangle is 2:3, respectively.
∴ Width = 2x units
and Length = 3x units
[tex]Area = Width \times length[/tex]
= [tex]2x\times 3x=6x^2[/tex] square units
now, if the width of the rectangle is increased by 50% and the length is increased by the same number of units
then width and length becomes
New width=2x+0.05(2x)=2x+x=3x units
and length=3x+3x=6x units
Therefore, [tex]New area=Width\times length[/tex]
= [tex]3x\times 6x=18x^2[/tex] square units
Area increased by percentage = [tex]\frac{New Area-Old Area}{Old Area}\times 100[/tex]
= [tex]\frac{18x^{2}-6x^{2}}{6x^{2}} \times 100=\frac{12x^{2} }{6x^{2}} \times 100[/tex]
= 200%
