Final answer:
To solve for the width of a rectangle when given the perimeter and length, subtract twice the length from the perimeter and divide by 2. Kara subtracted twice the length from the perimeter, getting 30, then divided by 2 to find the correct width of 15 cm, represented by Option 3.
Step-by-step explanation:
To find the width of a rectangle when you know the perimeter and the length, you first calculate the total length of both the length sides of the rectangle, then subtract this from the perimeter to find the total length of the two width sides. Finally, you divide this result by 2 to find the width of one side. According to the problem, the perimeter of the rectangle is 46 centimeters and the length is 8 centimeters.
Kara's method is correct: 46 minus 2 times 8 equals 30. This is because she first calculates the combined length of the two length sides (2 times 8 equals 16), and subtracts this from the total perimeter (46 - 16 equals 30) to find out the combined width of the two width sides. Then she divides by 2 to get the width of one side, which equals 15 centimeters, therefore Kara should choose Option 3: 15.
Kal's method is incorrect because he does not account for both lengths in his equation. He should have subtracted the total length from the perimeter before attempting to solve for the width.