Two Squares

Geometry Level 1

In the image above the yellow and the pink squares are overlapping in the orange region. The part of the yellow square that is not overlapping is equivalent 52% of their area. The part of the pink square that is no overlapping is equivalent to 73% of their area.

What the is the ratio between the side of the yellow square and the side of the pink square?

2 3 \frac {2}{3} 5 9 \frac {5}{9} 3 4 \frac {3}{4} 19 24 \frac {19}{24}

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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3 solutions

Serly Zubir
Jul 1, 2014

suppose that the side of the yellow square is x x , the side of the pink square is y y and the area of the orange is z z .

Since,

z = ( x 2 ) − ( 0.52 × x 2 ) z = (x^{2} ) - (0.52 \times x^{2} )

and

z = ( y 2 ) − ( 0.73 × y 2 ) z =( y^{2} )- (0.73 \times y^{2} ) .

Then, 0.48 × x 2 = 0.27 × y 2 0.48 \times x^{2} =0.27\times y^{2}

x 2 y 2 = 27 % 48 % \frac {x^{2}}{ y^{2}} =\frac{27\%}{48\%}

x y = 3 4 \frac{x}{y}=\frac{3}{4}

So, the ratio of the side of the yellow square and the side of the pink square is 3 4 \boxed {\frac {3}{4}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

But trail and error can also make it.one is small and one is big but common area percentage multiplied by the given side square(from options).=3/4

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Rohit Kumar
May 24, 2014

.48 area of yellow square=.27 area of pink square Area of pink=pxp Area of yellow=yxy yxy÷pxp=.27÷.48 y^2÷p^2=9/16 y/p=3/4

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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