Brain Teasers
St. George's Cross
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?
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?
Answer
21 cm wideHide Answer Show Answer
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Comments
I don't understand why this has such low difficulty. The answer is actually quite complex. I've submitted it as a correction.
not one of ur best teasers mad-ade. but i could be byast cuz i couldn't figure it out!!!!! good job anyway!!!!
The correction doesn't seem to have gone through Sane, so here goes!
Let x be the width of the cross. That leaves 4 corner pieces of white each measuring (91-x)/2 by (60 -x)/2.
The total white area is (91-x)(60-x).
The cross consists of 2 overlapping strips measuring 91x and 60x respectively. The red area is 91x+60x - x^2 (to remove the overlap).
So (91-x)(60-x) = 91x+60x-x^2
2730 - 151x +x^2 =151x - x^2
2x^2 - 302x + 5460 = 0
x^2 - 151x + 2730 = 0
(x - 130)(x - 21) = 0 Factorising
x = 21 or 130
Since it cannot be 130 as that is wider than the flag, then the width of the cross is 21 cm.
A good teaser which would have been even better with a posted solution (as opposed to answer only!)
Let x be the width of the cross. That leaves 4 corner pieces of white each measuring (91-x)/2 by (60 -x)/2.
The total white area is (91-x)(60-x).
The cross consists of 2 overlapping strips measuring 91x and 60x respectively. The red area is 91x+60x - x^2 (to remove the overlap).
So (91-x)(60-x) = 91x+60x-x^2
2730 - 151x +x^2 =151x - x^2
2x^2 - 302x + 5460 = 0
x^2 - 151x + 2730 = 0
(x - 130)(x - 21) = 0 Factorising
x = 21 or 130
Since it cannot be 130 as that is wider than the flag, then the width of the cross is 21 cm.
A good teaser which would have been even better with a posted solution (as opposed to answer only!)
Sorry - there is a mistake in the expansion of the brackets. It should read 5460 in the second line of algebra rather than 2730. The error is corrected on the next line so the solution stands.
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