Triangulation

Geometry Level 4

A triangle is divided into four parts by two straight lines as shown. The areas of the three parts are 3 , 7 3,7 and 7 7 . What is the area of the fourth area?


The answer is 18.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

From,

S 1 : ( S 2 + 7 ) = 3 : 7 S_1:(S_2+7)=3:7

S 2 : ( S 1 + 3 ) = 7 : 7 S_2:(S_1+3)=7:7

We get,

S 1 = 7.5 S_1=7.5 and S 2 = 10.5 S_2=10.5

So,

S 1 + S 2 = 7.5 + 10.5 = 18 S_1+S_2=7.5+10.5=18

4 Helpful 0 Interesting 0 Brilliant 0 Confused

If you give only ratios of areas, you cannot calculate the absolute value of an area from it. The areas have to be 3, 7, and 7, not just in that ratio.

Marta Reece - 4 years ago

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I think it is the same, the ratio can be the areas actually. but I edited the problem for clarity. .

A Former Brilliant Member - 4 years ago

Please explain. How you get the ratio

swabhiman nayak - 4 years ago

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