Difference between revisions of "1999 CEMC Gauss (Grade 8) Problems/Problem 18"

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The perimeter of the triangle is
 
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<math> \text{ (A) }\ 15 \qquad\text{ (B) }\ 30 \qquad\text{ (C) }\ 90 \qquad\text{ (D) }\ 45 \qquad\text{ (E) }\ 60 </math>   
 
<math> \text{ (A) }\ 15 \qquad\text{ (B) }\ 30 \qquad\text{ (C) }\ 90 \qquad\text{ (D) }\ 45 \qquad\text{ (E) }\ 60 </math>   
 
==Solution==
 
==Solution==

Latest revision as of 15:06, 18 June 2025

Problem

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


An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.


The perimeter of the triangle is

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

Solution

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