Question
Byron calculated the area of the rectangle as 22 square centimeters. What is the error in his reasoning and what is the correct answer.
It shows 61/2 cm for length and 4 1/2 cm.
It shows 61/2 cm for length and 4 1/2 cm.
Answers
GPT 3.5
The error in Byron's reasoning is that he multiplied the length and width incorrectly.
The correct calculation for the area of a rectangle is:
Area = length x width
Given that the length is 6 1/2 cm and the width is 4 1/2 cm, we first need to convert the mixed numbers to improper fractions:
6 1/2 cm = 13/2 cm
4 1/2 cm = 9/2 cm
Now, we can calculate the area:
Area = (13/2) cm x (9/2) cm
Area = 117/4 cm^2
Area = 29.25 cm^2
Therefore, the correct area of the rectangle is 29.25 square centimeters, not 22 square centimeters as calculated by Byron.
The correct calculation for the area of a rectangle is:
Area = length x width
Given that the length is 6 1/2 cm and the width is 4 1/2 cm, we first need to convert the mixed numbers to improper fractions:
6 1/2 cm = 13/2 cm
4 1/2 cm = 9/2 cm
Now, we can calculate the area:
Area = (13/2) cm x (9/2) cm
Area = 117/4 cm^2
Area = 29.25 cm^2
Therefore, the correct area of the rectangle is 29.25 square centimeters, not 22 square centimeters as calculated by Byron.