1. ## Area of a Rectangle!! Help please!!!

hey, so im trying to help my cousin with a math problem about finding the area of the rectangle. the problem says,

A point P is in the first quadrant of a coordinate plane on the line y = 7 - 3x. From the point P perpendiculars are drawn from both the x and y-axis. what is the largest possible area of the rectangle.

the answer in the book says 49/12 but could you help me out and show how its done thanks. sorry i dont have a graph on here

mathlete

2. I assume you drew the triangle and rectangle just to get a picture?.

The width of the rectangle is x and the height is y.

The area of the rectangle is A=xy.

We know y=-3x+7

So, the area is $\displaystyle A=x(-3x+7)=-3x^{2}+7x$

Now, by calc or $\displaystyle x=\frac{-b}{2a}$, we can solve for x.

$\displaystyle a=-3, \;\ b=7$

$\displaystyle \frac{-7}{2(-3)}=\frac{7}{6}$ is the width.

Plug this into y to find the height.

Then multiply the two answers to get the area. I bet you get 49/12.