Posted by **kayla** on Monday, August 30, 2010 at 3:19pm.

A rectangle has an area of 60 square inches and a perimeter of 38 inches. Find the length and width if the rectangle.

- math -
**Ms. Sue**, Monday, August 30, 2010 at 3:32pm
The dimensions for the area must be either

10 * 6

or

12 * 5

or

15 * 4

Which of those sets of dimensions will give you a perimeter of 38 inches?

Which

- math -
**Henry**, Monday, August 30, 2010 at 4:45pm
L * W = 60 sq in

W = 60/L

2L + 2W = 36 IN

Substitute 60/l for w:

2L + 2*60/L = 36

2L + 120/L = 36

Multiply both sides by L:

2L^2 + 120 = 36L

L^2 + 60 = 18L

L^2 - 18L + 60 = 0

Use Quadratic formula to find l:

L = 9 +- sqrt(21) = 9 +- 4.58

L = 13.58, and 4.42.

13.58 * W = 60, W = 4.42 IN

4.42 * W = 60, W = 13.57 in

2 Solutions: L * W =13.58 * 4.42 and

L * W = 4.42 * 13.58.

- math -
**Henry**, Monday, August 30, 2010 at 5:26pm
OOPS!! I used 36 for the perimeter.

It should be 38. Sue made the same error.

L * W = 60 IN^2, W = 60/L

2L + 2W = 38 IN

2L + 2 *60/L = 38

2L + 120/L = 38

2L^2 + 120 = 38L

L^2 + 60 = 19L

L^2 - 19L + 60 = 0

(L - 4) (L - 15) = 0

L = 4, and 15.

2 solutions: L = 4, W = 15.

L = 15 , W = 4.

- math -
**Henry**, Monday, August 30, 2010 at 5:31pm
NO, SUE DID NOT MAKE THE ERROR THAT

I MADE!

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