rectangle inscribed in a right triangle

[greenmath]

Hey this problem i have trouble doing:

Find the dimensions of the largers rectangle that can be inscribed in a right triangle bounded by the positive x and y axes and the line 2x+8y=8

im confused please help

 

[galactus]

Solve your line equation for y.

Then you will have it in the form y=mx+b

The area of the rectangle can be written as A=xy

Sub in your line equation for y and you will be entirely in terms of x.

Then you have a quadratic. Use x=-b/(2a) to find the x value and y will follow.