Question

A rectangle has length 8 cm. The rectangle has an area of 20 cm^2. The length of the rectangle is increased by 2 cm. The area of the rectangle is increased by 4 cm^2. Noah says, "The width of the rectangle decreases by less than 5%". Is Noah correct? You must show how you get your answer.

Options:
Option 1: Yes, Noah is correct.
Option 2: No, Noah is not correct.
Option 3: The change in width cannot be determined from the information given.
Option 4: Not enough information is provided to determine if Noah is correct.

Answer 1

Noah is correct about the width of the rectangle decreasing by less than 5% because it decreases from 2.5 cm to 2.4 cm, which is a 4% decrease.

Step-by-step explanation:

We need to determine if Noah is correct about the width of the rectangle decreasing by less than 5%. The original rectangle has a length of 8 cm and an area of 20 cm2 which gives us a width of 20 cm2 ÷ 8 cm = 2.5 cm. When the length is increased by 2 cm, the new length is 10 cm, and the area increases by 4 cm2 to 24 cm2. Therefore, the new width must be 24 cm2 ÷ 10 cm = 2.4 cm. The percent decrease in width is (2.5 cm - 2.4 cm) ÷ 2.5 cm = 0.1 cm ÷ 2.5 cm = 0.04, which is 4%. Since 4% is less than 5%, Noah is correct.