In the figure, △abc is congruent to △adc. if the square abcd is dilated by a factor of 2 to form a'b'c'd', what is the ratio of the area of a'b'c'd' to the area of abcd?

a) 2: 1
b) 3: 1
c) 4: 1
d) 5: 1

The answer to this question would be: c) 4:1

In this question, the square is dilated by a factor of 2 to form A'B'C'D'. That mean the new square sides will be twice as much as the old square. The formula for area is side^2. Then, the area of the new square should be

a'=2a

old square area= a*a= a^2
new square area= a'*a'= 2a*2a= 4a^2

new square area:old square area = 4a^2:a^2= 4:1

When rates are expressed as a quantity of 1, such as 2 feet per second or 5 miles per hour, they are called unit rates. if you have a multiple-unit rate such as 120 students for every 3 buses, and want to find the single-unit rate, write a ratio equal to the multiple-unit rate with 1 as the second term.