The length of a rectangle is 7 cm longer than its width. If the perimeter of the rectangle is 74cm, find the length and the area of the rectangle.
Step 1: Assign variables.
Let's assign "x" to represent the width of the rectangle.
Step 2: Set up an equation for the length.
Since the length is 7 cm longer than the width, it can be expressed as "x + 7".
Step 3: Write an equation for the perimeter.
The perimeter of a rectangle is calculated by adding up all the sides, which in this case is twice the length plus twice the width.
So the equation is: 2(x + (x + 7)) = 74
Step 4: Simplify the equation.
Expanding the brackets gives: 2(2x + 7) = 74
Simplifying further gives: 4x + 14 = 74
Step 5: Solve the equation.
Subtracting 14 from both sides gives: 4x = 60
Dividing both sides by 4 gives: x = 15
Step 6: Find the length and the area.
Using the value of x, the width of the rectangle is 15 cm.
The length is x + 7 = 15 + 7 = 22 cm.
The area of a rectangle is calculated by multiplying the length and width, so the area is: 15 cm * 22 cm = 330 cm².
Therefore, the length of the rectangle is 22 cm and the area is 330 cm².
To find the length and area of the rectangle, we can start by representing the width of the rectangle as "x" cm.
According to the problem, the length of the rectangle is 7 cm longer than its width. So, the length of the rectangle can be represented as "x + 7" cm.
The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, we have two equal sides (width) and two equal sides (length). Therefore, the perimeter can be calculated as:
Perimeter = 2 * (Width + Length)
74 = 2 * (x + x + 7)
74 = 2 * (2x + 7)
74 = 4x + 14
4x = 74 - 14
4x = 60
Now, divide both sides of the equation by 4 to solve for x:
4x / 4 = 60 / 4
x = 15
So, the width of the rectangle is 15 cm.
Using this information, we can find the length of the rectangle:
Length = Width + 7
Length = 15 + 7
Length = 22 cm
Therefore, the length of the rectangle is 22 cm.
To find the area of the rectangle, we can use the formula:
Area = Length * Width
Area = 22 * 15
Area = 330
Therefore, the area of the rectangle is 330 square cm.
Width is 15 feet and length is 22 feet
width-- x
length -- x+7
2x + 2(x+7) = 74
solve for x to width the width and length
Area = width x length