1. Rectangle ABCD has length 4 ft and width 9 ft. Rectangle PQRS is made by applying a scale factor of 5 to Rectangle ABCD.
(a) Are Rectangle ABCD and Rectangle PQRS similar? Why or why not?
(b) Calculate the area of Rectangle ABCD. Show all your work.
(c) Calculate the area of Rectangle PQRS. Show all your work.
(d) How does the area of Rectangle PQRS compare to Rectangle ABCD? Explain the relationship to the scale factor.
a) yes, the two rectangles are similar. this is because PQRS is made by applying a scale factor to ABCD, meaning that each side of PQRS has a constant ratio to ABCD.
(yikes, sorry if this explanation wasn't too good)
b) the area is simply length * width, which is 9*4 = 36.
c) the side lengths of PQRS are 9*5 = 45, and 4*5 = 20. the area of PQRS is 45*20 = 900.
d) the ratio of the area of ABCD to the area of PQRS is 36/900 = 1/25. this means that the area of PQRS is 25 times that of ABCD, which is also the square of the scale factor.
hope this helped! again, sorry if my explanations weren't that good. feel free to ask any further questions :)