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UKMT Senior Kangaroo, 2022

Geometry Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The perimeter of the square in the figure is 40. The perimeter of the larger equilateral triangle in the figure is $a + b\sqrt{p}$ , where $p$ is a prime number. What is the value of $7a + 5b + 3p$ ?

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