# Quadratic equation and algebra to solve geometrics

• Mar 1st 2007, 02:49 PM
stephie
Quadratic equation and algebra to solve geometrics
Hello
If anyone takes the time to read my questions, thanks a lot :)

1) A park is 480m long by 320 wide. It is decided to double its area retaining the rectangular shape, by adding strips of equal width to one end and one side. Find the length of the strips.

--> I thought iIwas doing this right by going (480+x)(320+x)= 2Area but in the end after doing the quadratic equation I somehow got a strange answer

2)A strip of metal 8cm wide is to be bent into a trough of rectanglular cross-section (open top) whose cross sectional area is 7.5cm2. Find the depth and width of the trough

Thanks a lot everybody:):)
• Mar 1st 2007, 04:40 PM
monsieur fatso
Quote:

Originally Posted by stephie
Hello
If anyone takes the time to read my questions, thanks a lot :)

1) A park is 480m long by 320 wide. It is decided to double its area retaining the rectangular shape, by adding strips of equal width to one end and one side. Find the length of the strips.

--> I thought iIwas doing this right by going (480+x)(320+x)= 2Area but in the end after doing the quadratic equation I somehow got a strange answer

Thanks a lot everybody:):)

I'm not sure if I'm reading this correctly, but I have a feeling that for the park to retain the same shape, the widths being added to each side would have to be different. You would have to keep the same ration between the two sides, so something like (480+x)(320+(2/3)x) = 2Area.

Hopefully I read the problem correctly, and hopefully this helps.
• Mar 1st 2007, 05:15 PM
topsquark
Quote:

Originally Posted by stephie
1) A park is 480m long by 320 wide. It is decided to double its area retaining the rectangular shape, by adding strips of equal width to one end and one side. Find the length of the strips.

--> I thought iIwas doing this right by going (480+x)(320+x)= 2Area but in the end after doing the quadratic equation I somehow got a strange answer

I'm not sure what strange answer you are getting, but you have the method.

(480 + x)(320 + x) = 2A = 2*480*320

x^2 + 800x + 480*320 = 2*480*320

x^2 + 800x - 480*320 = 0

x^2 + 800x - 153600 = 0

I'll admit it, I used the quadratic formula on this. But it DOES factor. Anyway, I get that x = 160 or x = -960. Thus there is only one possible answer: x = 160 m.

-Dan
• Mar 2nd 2007, 03:58 AM
Soroban
Hello, Stephie!

Did you make a sketch?

Quote:

2) A strip of metal 8cm wide is to be bent into a trough of rectanglular cross-section
(open top) whose cross sectional area is 7.5cm². .Find the depth and width of the trough.

Code:

```      *          *       |          |       |          |     d |          | d       |          |       |          |       * - - - - - *             w```

The strip of metal is 8 cm wide: .w + 2d .= .8

The cross-sectional area is 7.5 cm²: .wd .= .7.5

Now solve the system of equations.