## dmqrdh18 3 years ago Find the maximum area for a rectangle with the given perimeter 76 inches

1. freckles

Ok so what is the formula for perimeter of a rectangle?

2. freckles

|dw:1347998976956:dw|

3. freckles

Or give me the equation for the perimeter of that rectangle.

4. dmqrdh18

P= 2L+2W

5. dmqrdh18

The only number I have to work with is the perimeter of 76 inches

6. freckles

Right. So P=76

7. freckles

So we have 76=2x+2y

8. freckles

Now what is the area of the rectangle I drew. Or what is the formula for the area of a rectangle.

9. dmqrdh18

I'm not sure?

10. freckles

You know the area of a rectangle is Length * Height right?

11. dmqrdh18

Yes the length x width

12. freckles

So here my rectangle has length=y and height=x right So the area of the rectangle is?

13. freckles

Do you know the calculus way or the algebra was to maximize the area?

14. dmqrdh18

Would I take 76 divided by 4 ?

15. freckles

Can you do the shortcut way? Is that allowed?

16. dmqrdh18

Sure

17. freckles

Do you know why it works? Are you taking calculus or algebra? And yes if you have a=2l+2w and you want to maximize A then to find where you have maximum area you do a/4=w=l. But you haven't found the max area. You just found at what w and l you have max area. You told me area is length times width Just plug those values in for w and l and magic! you will have the answer.

18. dmqrdh18

Geometry

19. dmqrdh18

So it would be 19 for each side and times that by 2= 361

20. freckles

well you mean 19(19)=361 and yes that is correct great job! :)

21. dmqrdh18

Thanks