SOLUTION: A rectangle has length 15 cm and width y cm. If its perimeter is more than 50 cm but less than 70 cm, find the range of values of y. A. 10 < y < 14 B. 10 < y < 20 C. 20 < y

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Question 1126666: A rectangle has length 15 cm and width y cm. If its perimeter is more than 50 cm but less than 70 cm, find the range of values of y.
A. 10 < y < 14
B. 10 < y < 20
C. 20 < y < 30
D. 35 < y < 55
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

P = perimeter of rectangle
L = length = 15
W = width = y
P = 2*(L+W)
P = 2*(15+y)
P = 30+2y

Since the "perimeter is more than 50" we know that P > 50 or 50 < P.
At the same time we're told that the perimeter is "less than 70", so P < 70.
Combine 50 < P and P < 70 to get 50 < P < 70

50 < P < 70
50 < 30+2y < 70 Replace P with 30+2y
50-30 < 30+2y-30 < 70-30 subtract 30 from all sides
20 < 2y < 40
20/2 < 2y/2 < 40/2 divide all sides by 2
10 < y < 20

Answer: Choice B. 10 < y < 20
This means that y can be anything between 10 and 20 as long as it's not 10, and it's not 20 either.

SOLUTION: A rectangle has length 15 cm and width y cm. If its perimeter is more than 50 cm but less than 70 cm, find the range of values of y. A. 10 < y < 14 B. 10 < y < 20 C. 20 < y < 30