# geometry

the diagram below shoes a pennant in the shape of an isosceles triangle. the equal sides each measure 13, the altitude is x+7 and the base is 2x.

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1. Draw the figure

x^2 + (x+7)^2 = 13^2
x^2 + x^2 + 14x + 49 = 169
x^2 + 7x - 60 = 0
(x+12)(x-5) = 0

x = 5

sides are 13,13,10
altitude is 12, making the half-triangle a 5,12,13 triangle.

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