Question

Find all possible values of a and b in the figures

below, given these three conditions:
1. The perimeters are equal.
2. The rectangle has an area
between 80 and 100 square units.
3. The values of a and b are integers

Answer 1

Explanation:

The perimeters are equal, so

2a+2b = 4a+b

b = 2a

area of rectangle is between 80 and 100

80 < ab < 100

substitution

80 < a(2a) < 100

40 < a² < 50

√40 < a < √50

6.4 < a < 7.1

Since a is an integer, a = 7.

b = 2a = 14.