the perimeter of a rectangle is 24cm.express tha area of the rectangle in terms of width x
x(12-x)
To express the area of a rectangle in terms of its width, we need to understand the relationship between the perimeter and the dimensions of the rectangle.
The perimeter of a rectangle is given by the formula: P = 2l + 2w, where 'l' represents the length and 'w' represents the width of the rectangle.
In this case, we are given that the perimeter is 24 cm, so we can write the equation as: 24 = 2l + 2w.
To express the area of the rectangle in terms of width (x), we need to solve for the length in terms of x. Rearranging the perimeter equation, we have: 2l = 24 - 2w.
Dividing both sides of the equation by 2 gives us: l = 12 - w.
Now we can express the area of the rectangle in terms of width (x). The area of a rectangle is given by: A = l * w.
Substituting the value of l from the equation above, we get: A = (12 - w) * w.
Simplifying the expression: A = 12w - w^2.
Therefore, the area of the rectangle is given by the equation A = 12w - w^2 in terms of the width 'x'.