A rectangle picture frame has a perimeter of 1800 centimeters and a width that is 300 less than its length. Find the area of the picture.
P = 2L + 2W
1800 = 2L + 2(L - 300)
1800 = 4L - 600
2400 = 4L
600 = L
A = 600 * 300
Step 1: Let's assign variables to the unknowns. Let's call the length of the rectangle "L" and the width "W".
Step 2: We are given that the width is 300 less than the length, so we can write the equation W = L - 300.
Step 3: The formula for the perimeter of a rectangle is P = 2L + 2W. Since we know the perimeter is 1800 centimeters, we can substitute the values into the equation and solve for L.
1800 = 2L + 2(L - 300)
Step 4: Simplify the equation.
1800 = 2L + 2L - 600
Step 5: Combine like terms.
1800 = 4L - 600
Step 6: Add 600 to both sides.
1800 + 600 = 4L
2400 = 4L
Step 7: Divide both sides by 4.
2400/4 = L
600 = L
Step 8: Now that we have the length, we can substitute it back into the equation W = L - 300.
W = 600 - 300
W = 300
Step 9: Finally, we can calculate the area of the rectangle using the formula A = L × W.
A = 600 × 300
A = 180,000 square centimeters
So, the area of the picture is 180,000 square centimeters.
To find the area of the picture, we first need to determine the dimensions of the rectangle.
Let's assume the length of the rectangle is represented by 'L' centimeters.
According to the given information, the width is 300 centimeters less than the length, so the width would be 'L - 300' centimeters.
The perimeter of a rectangle is calculated by adding the lengths of all four sides, which in this case would be:
2(length) + 2(width) = 1800 cm
Substituting in the values we have:
2L + 2(L - 300) = 1800
Expanding the equation:
2L + 2L - 600 = 1800
Combining like terms:
4L - 600 = 1800
Adding 600 to both sides of the equation:
4L = 2400
Dividing both sides by 4:
L = 600
Now that we have the value for 'L', we can find the value of the width:
Width = L - 300 = 600 - 300 = 300
So, the dimensions of the rectangle are length = 600 cm and width = 300 cm.
To find the area, we multiply the length and width of the rectangle:
Area = Length × Width = 600 cm × 300 cm = 180,000 cm²
Therefore, the area of the picture is 180,000 square centimeters.