The width of a rectangle is 8 cm less than its length. The perimeter of the rectangle is 52 cm.
What is the width of the rectangle?
7 cm
9 cm
15 cm
17 cm
Perimeter of a rectangle is:
P=2l+2w
w=l-8
52=2l+2(l-8)
52=2l+2l-16
52=4l-16
4l=68
l=17
therefore
w=l-8,
w=17-8
w=9
To find the width of the rectangle, we need to set up an equation based on the given information. Let's assume that the length of the rectangle is "x" cm.
According to the problem, the width of the rectangle is 8 cm less than its length. So, the width is (x - 8) cm.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 52 cm.
The formula for the perimeter of a rectangle is: perimeter = 2(length + width)
Substituting the given values, we get:
52 = 2(x + (x - 8))
Simplifying the equation:
52 = 2(2x - 8)
52 = 4x - 16
4x = 52 + 16
4x = 68
x = 68/4
x = 17
Now, we know that the length of the rectangle is 17 cm.
To find the width, we can substitute the length back into the equation for the width:
Width = x - 8 = 17 - 8 = 9 cm
Therefore, the width of the rectangle is 9 cm.