Simple Geometry

Geometry Level 1

In the rectangle above, A B = B C AB=BC , C D D E \frac{CD}{DE} = 1 3 \frac{1}{3} , F G G A \frac{FG}{GA} = 1 3 \frac{1}{3} . What is the ratio of the area of B D E F G BDEFG to the area of the rectangle?

*Express the ratio as a decimal.

(This question was taken from one of my PSAT practice worksheets)


The answer is 0.75.

Fin Ko by Fin Ko , 18, USA

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1 solution

a r e a r e c t a n g l e = 4 ( 2 x ) = 8 x area~rectangle=4(2x)=8x

a r e a s h a d e d = 8 x − 1 2 ( 3 ) ( x ) − 1 2 ( 1 ) ( x ) = 6 x area~shaded=8x-\dfrac{1}{2}(3)(x)-\dfrac{1}{2}(1)(x)=6x

The ratio of the areas therefore is 6 x 8 x = \dfrac{6x}{8x}= 0.75 \boxed{0.75}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Another way is to put a value: say A B = B C = 3 AB=BC=3 .

A Former Brilliant Member - 3 years, 2 months ago

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