# Oxford PAT 2013, Question 10

## 5 thoughts on “Oxford PAT 2013, Question 10”

1. Will Cha says:

I think the area of large triangle has a little mistake; it’s not the answer but the steps. I think you use wrong equation. Could you explain this ?

1. You’re absolutely right, thanks for pointing it out. I have written the area of the big triangle as (a+c)d/2, when actually it is (a+c)d. But then when substituting in for the values of a, c, and d, I have actually used the proper formula so the answer for the large triangle is correct.

2. Hi Dan, thanks for your question.

The trick in this question is to observe that if you drop a perpendicular from one vertex of ab equilateral triangle to the opposite side, you get two 30-60-90 triangles. a is equal to 2r because the triangle whose hypotenuse is a is a 30-60-90 triangle. d is equal to 2r sqrt(3) because the triangle with sides a and d is another 30-60-90 triangle.

3. Dan says:

could you explain why a is equal to 2r and d is equal to 2r*3^(-1/2), please?