Answer:
The possible values of the perimeter of the rectangle is between 18 and
18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm
Explanation:
* Lets explain how to solve the problem
- The perimeter of any quadrilateral is the sum of the length of its
four sides
- The rectangle is a quadrilateral with each two opposite sides are
equal in lengths, then its perimeter = 2l + 2w, where l, w are its
length and width
∵ The the length of the rectangle is a
∵ 5.4 < a < 5.5 cm
∵ The perimeter of the rectangle = 2a + 2b
- Lets multiply the inequality by 2
∴ 5.4 × 2 < a × 2 < 5.5 × 2
∴ 10.8 < 2a < 11 ⇒ (1)
∵ The width of the rectangle is b
∵ 3.6 < b < 3.7 cm
- Lets multiply the inequality by 2
∴ 3.6 × 2 < b × 2 < 3.7 × 2
∴ 7.2 < 2b < 7.4 ⇒ (2)
- Add inequalities (1) and (2)
∵ 10.8 < 2a < 11
+ 7.2 < 2b < 7.4
∴ 18 < 2a + 2b < 18.4
∵ 2a + 2b represents the perimeter of the rectangle
∴ The possible values of the perimeter of the rectangle is between
18 and 18.4 cm ⇒ [18 < perimeter of rectangle < 18.4] cm