Difference between revisions of "2009 Grade 8 CEMC Gauss Problems/Problem 11"
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==Problem== | ==Problem== | ||
The perimeter of <math>\Delta ABC</math> is <math>32</math>. If <math>\angle ABC = \angle ACB</math> and <math>BC = 12</math>, the length of <math>AB</math> is | The perimeter of <math>\Delta ABC</math> is <math>32</math>. If <math>\angle ABC = \angle ACB</math> and <math>BC = 12</math>, the length of <math>AB</math> is | ||
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<math> \text{ (A) }\ 11 \qquad\text{ (B) }\ 10 \qquad\text{ (C) }\ 9 \qquad\text{ (D) }\ 12 \qquad\text{ (E) }\ 8 </math> | <math> \text{ (A) }\ 11 \qquad\text{ (B) }\ 10 \qquad\text{ (C) }\ 9 \qquad\text{ (D) }\ 12 \qquad\text{ (E) }\ 8 </math> | ||
==Solution 1== | ==Solution 1== | ||
Latest revision as of 10:04, 19 June 2025
Problem
The perimeter of 
is 
. If 
and 
, the length of 
is
An image is supposed to go here. You can help us out by creating one and editing it in. Thanks.
Solution 1
Since , the triangle is an isosceles triangle, where 
. That means that we can let 
represent and 
.
The perimeter is the sum of the side lengths of a polygon, meaning we can set up an equation:
~anabel.disher
Solution 2 (answer choices)
We can test answer choices, and see whether or not the side length results in the perimeter being too high or too low.
We can first use 
, and we get:
This happens to be exactly the perimeter of the triangle, so the answer is 
~anabel.disher
