Area of a triangle

Geometry Level 2

The area of the green region is 25 25 % of the sum of the areas of the green region and the blue region. Find the length of D C DC rounded to 1 decimal place.


The answer is 57.5.

A Former Brilliant Member by A Former Brilliant Member

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3 solutions

Michael Mendrin
Apr 1, 2017

Let altitude of the triangle be proportional to length along AB. Then solve for DC

0.25 ( 1 2 90 ⋅ 65 k ) = 1 2 ( 90 − D C ) 45 k 0.25\left( \dfrac { 1 }{ 2 } 90\cdot 65k \right) =\dfrac { 1 }{ 2 } \left( 90-DC \right) 45k

and get D C = 57.5 DC=57.5

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Using similar triangles, we have

45 ( 90 − D C ) = 0.25 ( 65 ) ( 90 ) 45(90-DC)=0.25(65)(90)

4050 − 45 D C = 1462.5 4050-45DC=1462.5

45 D C = 2587.5 45DC=2587.5

D C = 57.5 \boxed{DC=57.5}

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