math word problem

Question

A corner lot has dimensions 25 by 40 yards. The city plans to take a strip of uniform width along the two sides bordering the streets to widen these roads. How wide should the strip be if the remainder of the lot is to have an area of 844 square yards? (Round your answer to two decimal places.)

Answer 1

Hi Hannah

 

We have a rectanglar lot 25yd by 40yd

 

This is 1000 sq yds

The city will take a strip of land on two sides of this rectangle.

The remaining lot will be 844 sq yd

 

Now to set this up.

 

844 = (25-x)(40-x) 

where x is the width of the strip of land taken to widen the road

 

844 = 1000 - 65x + x²

 

Subtract 844 from both sides to set quadratic equal to 0.

x² - 65x + 156 = 0

 

Now we can factor by using the quadratic formula

-b±√(b²-4ac)

---------------

       2a

 

+65±√(65²-4*1*156)

-------------------------

           2*1

 

65±√(4225-624)

-------------------

           2

 

65±√3601

------------

      2

 

65±60

-------

   2

 

x = 5/2, 125/2

x = 2.5, 62.5

 

62.5 is an impossible answer.  You cannot take 62.5 yards away from 40 yards or 25 yards.

 

So the strip will be approximately 2.5 yards.