Daily Maths Challenges

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Find a+b (lemmy.world)

submitted 6 months ago* (last edited 6 months ago) by [email protected] to c/[email protected]

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The image is of a large unit square with five smaller disjoint shaded squares contained entirely within it. The five smaller squares are congruent. Four of them are at each corner of the large square. The fifth is in the center, rotated diagonally, so the center of each of its sides is touched by the vertex from one of the other four squares. You are given that the common length for the five smaller congruent squares is (a-sqrt(2)) / b, where a and b are positive integers. What is the value of a + b?

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[–] [email protected] 5 points 6 months ago (1 children)

holdup taking the side length of the unit square actually makes the working out a bit simpler, because the otherside is 1

idk i just saw the diagonal at first

2l+0.5 sqrt(2l^2)=1
l(2+0.5sqrt(2))=1
l=1/(2+0.5sqrt(2))
=(2-0.5sqrt(2))/3.5
=(4-sqrt(2))/7

also, all the public items on the drive is mean to be public, there are unlisted and private items u dont see

[–] [email protected] 3 points 6 months ago

Hey, you're right. I'm not sure what I did originally to make it so complicated, then ¯\_(ツ)_/¯