Area. The perimeter of a rectangle is 197 inches. If the rectangle is x inches wide, write a function for the area A(x).

I'm a little bit confused any help?

Question

Area. The perimeter of a rectangle is 197 inches. If the rectangle is x inches wide, write a function for the area A(x). 

I'm a little bit confused any help?

anonymous · Answer

@Luigi0210

jhannybean · Answer

Perimeter of a rectangle can be found by using the formula $$\large P=2l+2w$$ where l=length and w=width. 

They give you the width. width = w = x and P= 197. 
So our new equation for perimeter after inputting all the variables would be $$\large 197=2l+2x$$ we can solve for $l$ by subtracting 2x from both sides and dividing by 2. We will get $$\large l=\frac{-2x+197}{2}= -x +\cfrac{197}{2}$$ Now we can substitute $l$ into the equation for Area of a rectangle, which is : $\large A = l \cdot w$ Substituting $l$ back into our equation, we get $$\large A = \left(-x+\cfrac{197}{2}\right)(x)$$$$\large A=-x^2 +\cfrac{197}{2}x$$

anonymous · Answer

thanks so much. i really do appreciate your help and explanations...i had 2421ft^2 which is the area....but i don't think they were asking that

jhannybean · Answer

Yeah just a general equation