Respuesta :
Answer:
The percentage increase in Area of rectangle is 200%
Step-by-step explanation:
Given as :
The ratio of the width to the length of a rectangle is 2:3
Let The length of rectangle = 2 x
Let The width of rectangle = 3 x
∵ Area of rectangle = length × width
So, [tex]A_1[/tex] = 2 x × 3 x
Or, [tex]A_1[/tex] = 6 x²
Again
The increased length of rectangle = 2 x + 2 x = 4 x
The increase width of rectangle = 3 x + 50% of 3 x
I.e The increase width of rectangle = 3 x + 1.5 x = 4.5 x
∵ Increased Area of rectangle = increased length × increased width
Or, [tex]A_2[/tex] = 4 x × 4.5 x = 18 x²
So, The percentage increase in area = [tex]\dfrac{A_2 - A_1}{A_1}[/tex] × 100
Or, The percentage increase in area = [tex]\frac{18 x^{2}-6x^{2}}{6x^{2}}[/tex] × 100
Or , The percentage increase in area = [tex]\dfrac{12}{6}[/tex] × 100
∴ The percentage increase in area = 200
Hence, The percentage increase in Area of rectangle is 200% Answer
