Question

The perimeter of a rectangle is 14m and the length is x m. Express the breadth of the rectangle in terms of x.

Answer 1

Answer:

If the length of one side of the rectangle is x, then the side opposite and parallel to it also has a length of x. Since the perimeter of the rectangle is 20, then the other two sides have a measure of (20 - 2x), and each one has a measure of (20 - 2x)/2 = 10 - x.

The area of a rectangle = length x width = x(10 - x) = 10x - x²

The maximum area can be found by computing the derivative of the area formula

f(x) = 10x - x²

f'(x) = 10 - 2x

Find the critical points. Since f'(x) is defined for all real x, then the critical points occur where f'(x) = 0

10 - 2x = 0

10 = 2x

x = 5

So the other side = 10 - x = 10 - 5 = 5

The maximum area is 5 x 5 = 25 m²

Answer 2

Answer:

perimeter is 14

perimeter =2(l+b)

l=x and b=14-x