the length of a rectangle is 8 in more than its width. the perimeter of the rectangle is 54 cm. what are the width and length of the rectangle?
2 w + 2(w+8) = 54
4 w + 16 = 54
4 w = 38
You know:
l = w + 8
P = 54 = 2(w + l)
plug w + 8 in to the perimeter equation
To find the width and length of the rectangle, we can set up a system of equations using the given information.
Let's assume that the width of the rectangle is "x" inches. According to the problem, the length of the rectangle is "8 inches more than its width." So, the length can be represented as "x + 8" inches.
The perimeter of a rectangle can be calculated by adding the lengths of all its sides. In this case, the perimeter is given as 54 cm, which means that the sum of the lengths of all the sides is 54 cm.
Now, we can set up the equation for the perimeter:
2 * (width + length) = perimeter
Substituting the values:
2 * (x + x + 8) = 54
Simplifying the equation:
2 * (2x + 8) = 54
4x + 16 = 54
Subtracting 16 from both sides of the equation:
4x = 54 - 16
4x = 38
Dividing both sides of the equation by 4:
x = 38 / 4
x = 9.5
So, the width of the rectangle is 9.5 cm.
Now, to find the length, we can substitute the value of the width (x) into the expression for the length:
length = x + 8
length = 9.5 + 8
length = 17.5
Therefore, the length of the rectangle is 17.5 cm.
In summary, the width of the rectangle is 9.5 cm, and the length is 17.5 cm.