To make a cell phone protector, a company uses plastic rectangles 6 centimeters by 10 centimeters. Then squares x centimeters wide are cut from each corner.
Use the drop-down menus below to complete statements using words and symbols to describe the area in square centimeters of the remaining plastic.
Using Words
The area of the remaining plastic is given by the difference: __________ .
Using Symbols
The area of the remaining plastic is given by the difference: __________ cm² – __________ cm².
To find the area of the remaining plastic after cutting out squares from the corners, we first need to determine the dimensions of the remaining rectangle after the squares are removed.
1. Original area: The area of the original rectangle is calculated as:
[
text{Area} = text{length} times text{width} = 10 text{ cm} times 6 text{ cm} = 60 text{ cm}².
]
2. New dimensions after cutting squares: After cutting out squares with side length (x) from each corner, the new dimensions of the rectangle become:
– New length = (10 – 2x) (because squares are removed from both ends of the length)
– New width = (6 – 2x) (because squares are removed from both ends of the width)
3. Area of the remaining rectangle: The area of the remaining plastic is calculated as:
[
text{Remaining area} = (10 – 2x)(6 – 2x).
]
Using this information, we can complete the statements:
Using Words
The area of the remaining plastic is given by the difference: the original area minus the total area of the cut squares.
Using Symbols
The area of the remaining plastic is given by the difference: 60 cm² – (4x²), where (4