Answer:
Part 1) The length of the new rectangle is
Part 2) The area of the new rectangle is
Step-by-step explanation:
we know that
If two rectangles are similar, then the ratio of its corresponding sides is proportional
step 1
Find the length of the new rectangle
Let
L-----> the length of the new rectangle
step 2
Find the area of the new rectangle
we know that
The area of the rectangle is
we have
substitute
It represents a geometric sequence because it has a common ratio of 2.
In fact, a sequence is said to be geometric if any two adjacent elements are in the same ratio. In other words, if you choose any index and consider the two consecutive terms
and
, you have
no matter which index you chose. In your case, the next term in the sequence is always the double of the previous one, so the ratio between two consecutive terms is always 2, and the series is geometric with common ratio 2