Exercise:- A new flag design.
The flag measures 100cm by 90cm. The flag consists of a red cross with a white background. The thickness of the vertical strip is twice that of the horizontal one.
The area of the cross is half the area of the flag.
By making an equation or otherwise determine the thickness of the vertical strip.
area of whole flag = 9000 cm^2
width of thin stripe --- x
width of thicker stripe --- 2x
area of stripes = 2x(90) + x(100) - 2x^2
( we have to subtract the intersection of the stripes or else we would count it twice)
= 280x - 2x^2
4500 = 280x - 2x^2
2x^2 - 280x + 4500 = 0
x^2 - 140x + 2250 = 0
I will complete the square instead of using the formula
x^2 - 140x + 4900 = 4900-2250
(x-70)^2 = 2650
x = 70 ± √2650 = appr 18.5 or 121.5
but clearly x < 50
so x = appr 18.5 cm
so the vertical strip is 2x cm wide or appr 37 cm