SOLUTION: A farmer planted a trial poppy crop in a rectangular plot 40 metres long and 35 metres wide. The trial was successful, so the next year the farmer decides to increase the poppy plo

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Question 1144639: A farmer planted a trial poppy crop in a rectangular plot 40 metres long and 35 metres wide. The trial was successful, so the next year the farmer decides to increase the poppy plot by a further 1000 square metres. To do this the farmer increases the width of the plot by x metres and the length of the plot by 4x metres.
a) Draw a diagram with the following information
b) What is the total area (in m^2) of the larger poppy plot?
c) Write an equation, in standard quadratic form, to describe the area of the larger poppy plot in terms of x.
d) Using your equation in part c), apply algebraic techniques to find the dimensions (length and width) of the larger poppy plot.
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


(a) You can draw the diagram....

(b) (40*35)+1000 = 1400+1000 = 2400

(c) (40+4x)(35+x) = 2400

(d)
%2840%2B4x%29%2835%2Bx%29+=+2400 original equation
%2810%2Bx%29%2835%2Bx%29+=+600 factor out the common factor of 4 from the first expression to keep the numbers smaller
x%5E2%2B45x%2B350+=+600
x%5E2%2B45x-250+=+0
%28x%2B50%29%28x-5%29+=+0
x+=+-50 or x+=+5

Clearly the -50 makes no sense in the problem; so x=5.

The dimensions of the large field are
length: 40+4(5) = 60
width: 35+5 = 40