SOLUTION: Given a rectangle whose length is always 5 times of its width. Express the area A of this rectangle in a function of its perimeter . Step1: Assume that the length and width of

Question 121887: Given a rectangle whose length is always 5 times of its width. Express the area A of this rectangle in a function of its perimeter .
Step1: Assume that the length and width of the rectangle are L and W respectively. Then can be expressed in terms of , i.e. Express L and W as functions of X:

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The perimeter of a rectangle is given by , but we are given that the dimensions of this rectangle always have the relationship , so let's use that information to express the perimeter in terms of just W:

But now we can express the width, W, in terms of P by dividing by 12:

The area of a rectangle is given by , but we still know that , so the area of this rectangle is or

But we have developed an expression for W in terms of the perimeter, P, so let's substitute that for W in the area equation:

, or

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