Answer: The perimeter of a rectangle is the sum of all four sides. If the perimeter of the rectangle is 48 cm, that means that the sum of the length and width of the rectangle, multiplied by 2, is equal to 48.
Given that the length is 8 more than 3 times the width, we can set up the following equation:
length = 3 * width + 8
We can also use the area formula, which states that the area of a rectangle is equal to the product of the length and width. Let's call the width "w" and the length "l".
area = l * w
We can substitute the equation for length into the area equation:
area = (3w + 8) * w
We know the area of the rectangle, so we can substitute that in too:
area = (3w + 8) * w = 48
To find the width and length, we need to solve this equation for "w" and then substitute "w" back into the equation for "length". This will give us the width and length of the rectangle.
Explanation: