WMC 2018 Pursuit - Pack 2, D3

Geometry Level 2

Given rectangle A B C D ABCD , two lines are drawn parallel to sides A B AB and A D AD respectively. If the area of region I I is 3 and the area of region I I II is 27, compute the least possible area for A B C D ABCD .

WMC Pursuit Questions


The answer is 48.

Julian Yu by Julian Yu , 19, Philippines

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1 solution

X X
Oct 5, 2018

The product of the other two areas(let it be I I I III and I I I I IIII ) is equal to I × I I = 81 I\times II=81 .

So I I I × I I I I = 81 III\times IIII=81 , the minimum value of I I I + I I I I III+IIII obviously occurs at I I I = I I I I III=IIII .

The sum of the four areas = 3 + 9 + 9 + 27 = 48 =3+9+9+27=48

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