2014 CEMC Gauss (Grade 8) Problems/Problem 8

Problem

The perimeter of the isosceles triangle shown is $53$ cm.

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The value of $x$ is

$\text{ (A) }\ 11\qquad\text{ (B) }\ 21\qquad\text{ (C) }\ 20\qquad\text{ (D) }\ 19\qquad\text{ (E) }\ 31$

Solution

As shown from the diagram that shows which sides of the isosceles triangle are equal to each other, we have two sides that are equal to $x$ as well as a side that is equal to $11$ .

The sum of the three side lengths of the triangle will be equal to the triangle's perimeter.

Thus, we have:

$x + x + 11 = 53$

$2x = 42$

$x = \boxed {\textbf {(B) } 21}$

~anabel.disher

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2014 CEMC Gauss (Grade 8) Problems/Problem 8

Problem

Solution