SOLUTION: A rectangular field originally has dimensions 65m by 35m. Its area is reduced by removing a strip of equal width from the east and the north sides. The area of the new field is 1

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Question 1103578: A rectangular field originally has dimensions 65m by 35m. Its area is reduced by removing a strip of equal width from the east and the north sides. The area of the new field is 1000 square meters. Write a quadratic equation to model this situation. Use ‘x’ for the width of the strips removed. Solve the equation to find the dimensions of the new field.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52778)   (Show Source): You can put this solution on YOUR website!
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Let "w" be the wide of the removed strip.


Then the new dimensions of the reduced field are 65-w meters by 35-w meters.


The area of the new rectangle is  (65-w)*(35-w),  and the equation to find w is

(65-w)*(35-w) = 1000.     (*)


You can solve this equation MENTALLY by noticing that the difference of the original dimensions is 65-35 = 30 m 
and noticing that the difference of the reduced dimensions is the same 30 m.


So all you need is to find two factors of 1000 with the difference between them of 30,

and it is EASY: 50 and 20.


Thus  65-w = 50,  which implies  w = 65-50 = 15.


New dimensions are 65- 15 = 50 m  and  35-15 = 20 m.

Solved.

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Surely, you still have an alternative approach solving the quadratic equation (*).



Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
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..., by removing a strip of equal width from the east and the north sides.
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Notice that the two factors for 1000 differ by 30. You might try to use that.

Otherwise,


-
discriminant



New dimensions: 50 meters by 20 meters
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