Question

George is trying to draw a rectangle with a perimeter of 24 cm. He drew a base of 20 cm. Is there a possible height he can draw with that base to make a rectangle with a perimeter of 24 cm? Explain your thinking.

Answer 1

No, it is not possible for George to draw a rectangle with a 20 cm base and a perimeter of 24 cm, as this would require a negative height, which is impossible for a real rectangle.

Step-by-step explanation:

George wants to draw a rectangle with a perimeter of 24 cm and has chosen a base of 20 cm. To determine if this is possible, we can use the formula for the perimeter of a rectangle, which is:

P = 2×(length + width)

Substituting the given values, we have:

24 cm = 2×(20 cm + height)

To find the possible height, we divide both sides by 2:

12 cm = 20 cm + height

Then we can solve for height:

Height = 12 cm - 20 cm

Height = -8 cm

As height cannot be negative in a real-world scenario, it is impossible for George to draw a rectangle with a 20 cm base that has a perimeter of 24 cm. The base must be shorter to achieve a positive value for the height and make a rectangle with the given perimeter.