Triangles inside a square

Geometry Level 2

The above figure is a square and the given values are the areas of each triangle. If y , r y,r and b b represent the areas of the yellow, red and blue regions, respectively, find r + b − y r+b-y .


The answer is 0.

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2 solutions

Chew-Seong Cheong
Apr 13, 2017

Let the area of the square be A A . We note that:

{ 30.625 + y + 3.75 = 1 2 A 30.625 + r + b + 3.75 = 1 2 A ⟹ y = r + b ⟹ r + b − y = 0 \begin{cases} 30.625+y+3.75 & = \frac 12 A \\ 30.625+r+b+3.75 & = \frac 12 A \end{cases} \implies y = r+b \implies r+b - y = \boxed{0}

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Did the same way

Fidel Simanjuntak - 4 years, 1 month ago

Since the figure is a square, we have that

r + 30.625 + b + 3.75 = y + 30.625 + 3.75 r+30.625+b+3.75=y+30.625+3.75 ⟹ \implies r + b = y r+b=y ⟹ \implies r + b − y = 0 r+b-y=0 .

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