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

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) (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)
original equation
factor out the common factor of 4 from the first expression to keep the numbers smaller

or

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
RELATED QUESTIONS
A farmer wishes to fence his rectangular paddock, if its measurements are 366 metres long (answered by satyareddy22)

A farmer has 300 square metres of land suitable for cultivating the crops baigan, bodi,... (answered by mananth)

How many square metres in a rectangle x metres long and 3 metres wide? (answered by richard1234)

A farmer has a triangular field with sides that measure 40 metres (side AB), 35 metres... (answered by Alan3354)

what is the volume of a rectangular water tank which is 8 metres long 4 metres wide and 3 (answered by Tatiana_Stebko)

A rectangular field 50 metres wide and x metres long require 260 metres of fencing. Write (answered by ikleyn)

how do you work out how many square metres in a rectangle x metres long and 3 metres... (answered by mananth)

A swimming pool 100 metres long and 40 metres wide is 1 metre deep at the shallow end... (answered by checkley77,Alan3354)

A rectangular carpet is x metres long and 3 metres wide. Find a formula for its'... (answered by swincher4391)