1999 CEMC Gauss (Grade 8) Problems/Problem 18

Problem

The equilateral triangle has sides of $2x$ and $x + 15$ as shown.

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The perimeter of the triangle is

$\text{ (A) }\ 15 \qquad\text{ (B) }\ 30 \qquad\text{ (C) }\ 90 \qquad\text{ (D) }\ 45 \qquad\text{ (E) }\ 60$

By the definition of an equilateral triangle, all sides of the triangle must be equal to each other. This means that we have:

$2x = x + 15$

Subtracting $x$ from both sides, we get:

$x = 15$

The perimeter of an equilateral triangle is $3$ times its side length, so the perimeter is

$2x \times 3 = 6x = 6 \times 15 = \boxed {\textbf {(C) } 90}$

~anabel.disher