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Intermediate

Two of a kind

The red and blue triangles are similar. The white areas are given. What is the total area?

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Solution

The total area is 8.

First we name the parallel sides as shown, using the similarity of the red and blue triangles. From the triangle area formula A=absin(α)/2, we deduce that the large triangle is x2A, but als that 2=xA.

Now from comparing the similar triangles with base b and xb, we get x2 =A+3. We have two equations with variables x and A. They can be solved to give A=1 and x=2, leading to a total area of 8.

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