Question 2:- The length of a rectangle is three times its width. A new rectangle is created by decreasing the length of the original rectangle by 9 feet and increasing its width by 4 feet. The area of the new rectangle is the same as the area of the original rectangle. What is the perimeter of the new rectanle ?
Solution:- Let the width of the rectangle = w feet
Length of the length of rectangle = 3 w feet
Area of the recangle = w × 3w = 3 w² square feet
New length of recangle = (3w – 9) feet
New breadth of the recangle = (w + 4) feet
New area of the recangle = (3w – 9)(w + 4) square feet
According to the question
3 w² = (3w – 9)(w + 4)
⇒ 3 w² = 3 w² + 12w – 9w – 36
⇒ 0 = 3w – 36
⇒ w = 12
Length of new recangle = 3w – 9 = 3×12 – 9 = 27
Breadth of new recangle = w + 4 = 12 + 4 = 16
Total perimeter of new recangle = 2(27 + 16)
= 86 feet
Question 1:- A streaming video service offers its customers two plans. The first plan has a $ 24 registration fee, a fixed monthly rate of $5 and a charge of $0.75 for each video download. The second plan has a $15 registration fee, a fixed monthly rate of $3 and a charge of $1.50 for each vedio download. For how many download would the two plans cost the same for a year of service ?
Solution:- See full solution