A playground, which measures 50m by 35m, is to be doubled in area by adding a strip of uniform width around the outside of the existing area. What is the width of the new strip around the playground?

With problems of this type it becomes much clearer if you do a quick sketch.

The inner area is #35 mxx50 m=1750 m^3#

The outer strip area is
#4x^2+(2xx35x)+(2xx50x)=4x^2+170x#

Combining the outer strip and the inner area doubles the inner area. So our model becomes:

#4x^2+170x+1750 = (2xx1750)#

#4x^2+170x+1750 = 3500#

Subtract 3500 from both sides

#4x^2+170x-1750 = 0#

Simplifying the numbers a bit. 4 will not divide exactly into 1750. However, all the numbers are even so we can at least halve them

#2x^2+85x-875=0#

If you can not spot the whole number factors quickly don't waste time in an exam continuing to try and determine them. Use the formula.

#x=(-b+-sqrt(b^2-4ac))/(2a)color(white)("dd")->color(white)("dd") (-85+-sqrt(85^2-4(2)(-875)))/(2(2))#

#x= (-85+-sqrt(14225 ))/4#

#x= (-85+-sqrt(5^2xx569 ))/4 larr" Note that 569 is a prime number"#

#x=(-85+-5sqrt(569))/4 larr" Exact values"#

The negative final value is not logical so is dismissed.

#x=(-85+5sqrt(569))/4 larr" Exact solution"#

#x~~ 8.567151....#

#x=(-85+5sqrt(569))/4~~8.567# to 3 decimal places