The length of the rectangle is 5 cm longer than its width. If the perimeter is 46 cm, what is the area?
I am confused…
To solve this problem, we need to make use of the given information and apply the formulas for the perimeter and area of a rectangle.
Let's let 'x' represent the width of the rectangle.
Given that the length is 5 cm longer than the width, the length would be x + 5.
The perimeter of a rectangle is given by the formula: 2(length + width).
In this case, the perimeter is given as 46 cm, so we can set up the equation:
2(x + (x + 5)) = 46
Simplifying the equation, we get:
2(2x + 5) = 46
Expanding the brackets, we have:
4x + 10 = 46
Subtracting 10 from both sides, we have:
4x = 36
Dividing both sides by 4, we get:
x = 9
So the width of the rectangle is 9 cm, and the length would be 9 + 5 = 14 cm.
The area of a rectangle is given by the formula: length × width.
Therefore, the area of this rectangle is:
9 cm × 14 cm = 126 square cm.
So, the area of the rectangle is 126 square cm.
To find the area of a rectangle, we need to know its length and width.
Let's assume that the width of the rectangle is "x" cm.
According to the problem, the length of the rectangle is 5 cm longer than its width, so the length would be (x + 5) cm.
The formula for the perimeter of a rectangle is:
Perimeter = 2(length + width)
Given that the perimeter is 46 cm, we can substitute the values into the formula and solve the equation for x.
46 = 2((x + 5) + x)
Now, let's solve for x:
46 = 2(2x + 5)
46 = 4x + 10
4x = 46 - 10
4x = 36
x = 9
So, the width of the rectangle is 9 cm.
Now, we can find the length by adding 5 to the width:
Length = x + 5 = 9 + 5 = 14 cm
To find the area of the rectangle, we use the formula:
Area = length × width
Area = 14 cm × 9 cm
Area = 126 cm^2
Therefore, the area of the rectangle is 126 square centimeters.
2w+2L = 46
so
w+L = 23
L = w+5
so
w + w + 5 = 23
2 w = 18
w = 9
then L = 14