The length of the hole x is 5 cm, and the length of the metal sheet y is 6 cm.
Let's solve the problem step by step:
Step 1: Define the Variables
- Let x be the width of the rectangular hole.
- Let y be the length of the metal sheet.
Step 2: Express the Given Information in Equations
- The width of the metal sheet is 5 cm, so y = 5 cm.
- The length of the metal sheet is y cm.
- The width of the hole is 2 cm.
- The length of the hole is x cm, and it is 1 cm less than the length of the metal sheet, so x = y - 1 .
Step 3: Express the Remaining Area of the Metal Sheet
- The area of the metal sheet before cutting the hole is 5y square centimeters.
- The area of the hole is 2x square centimeters.
- The remaining area after cutting the hole is 5y - 2x square centimeters.
Step 4: Write the Equation for the Remaining Area
- The problem states that the remaining area is 20 square centimeters. Therefore, we can write the equation:
5y - 2x = 20
Step 5: Substitute the Expression for x from Step 2 into the Equation
- Substitute x = y - 1 into the equation:
5y - 2(y - 1) = 20
Step 6: Solve for y
- Expand and simplify the equation:
5y - 2y + 2 = 20
3y + 2 = 20
3y = 18
y = 6
Step 7: Substitute the Value of y back into the Expression for x from Step 2
- x = y - 1 = 6 - 1 = 5
Step 8: Check the Solution
- Ensure that the solution satisfies the original condition that the remaining area is 20 square centimeters:
5(6) - 2(5) = 30 - 10 = 20
Step 9: Provide the Final Answer
- The length of the hole x is 5 cm, and the length of the metal sheet y is 6 cm.
Therefore, the solution is x = 5 cm and y = 6 cm.
The probable question can be: A rectangular hole 2 cm wide and x cm long is cut in a rectangular sheet of metal that is 5 cm wide and y cm long. The length of the hole is 1 cm less than the length of the metal sheet. After the hole is cut, the area of the remaining metal sheet is 20 cm squared.
Find the length of the hole(x) and the length of the metal sheet (y).