A geometry problem by Syed Baqir
The drawing is of the flag of St. George.
It consists of a red cross on a white background.
Both arms of the red cross are the same width.
The flag measures 60 cm by 91 cm.
If the area of the red arms is equal to the area of white,
what should be the width of the red arms (in cm)?
The answer is 21.
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Total Area of Rectangle = 60 * 91 = 5460 c{ m }^{ 2 }
Hence we can conclude :
Total Area - Red Area - White Area = 0
Since , Red Area = White Area,
Therefore, Total Area - 2 Red Area = 0 ==> Total Area = 2 Red Area
Let w be the width of Red Arms and since they are same so we have one variable w.
Red Area = Area of Rectangle Vertical + Area of Red Rectangle - Area of square
5460 = 2 ( 60w + 91 w - w 2 )
After simplification: -2 w 2 + 302 w -5460 =0
Using quadratic Formula:
We get w =21