Triangles and squares

Geometry Level 2

Triangles A B C ABC and X Y Z XYZ are congruent right angled isosceles triangles. Squares blue and red are as shown. If the area of blue square is 189 189 . What is the area of the red square?


The answer is 168.

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1 solution

David Vreken
Dec 18, 2018

A B C \triangle ABC can be split into 4 4 equal triangles and X Y Z \triangle XYZ can be split into 9 9 equal triangles

Since the blue square is 1 2 \frac{1}{2} of the whole triangle, the area of the whole triangle is 2 189 = 378 2 \cdot 189 = 378 .

Since the red square is 4 9 \frac{4}{9} of the whole triangle, the area of the red square is 4 9 378 = 168 \frac{4}{9} \cdot 378 = \boxed{168} .

I used the same method!

Victor Paes Plinio - 2 years, 5 months ago

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