perimeter of a triangle

khansaheb said:
show us your effort/s to solve this problem.
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👍

The Highlander said:
You're not serious about this one, are you?
How would you find the perimeter of any shape?
Add the lengths of all the sides together (and, in this case, then simplify!)
🤷‍♂️
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Thanks The Highlander for providing some valuable hints.

Here is my strategy to attack this problem.

Let \(\displaystyle S_i\) be the length of one triangle leg, then the perimeter of the triangle is:

\(\displaystyle S_1 + S_2 + S_3 = 3x - 2 + 2x + 3 + 5x = 10x + 1\)

Next, ask yourself: is it possible to find the value of \(\displaystyle x\) from the given information in the OP?
🤔

Yes, it is possible. If the triangle has two equal angles, it means that it has two equal sides.

Then

\(\displaystyle 3x - 2 = 2x + 3\)
\(\displaystyle 3x - 2x = 3 + 2\)
\(\displaystyle x = 5\)

This means that the perimeter of the triangle is \(\displaystyle 10x + 1 = 10(5) + 1 = 50 + 1 = 51\)
 
logistic_guy said:
What is the perimeter of the triangle?

View attachment 38994
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What a frustrating thread! Did anyone else notice the red arcs which indicate congruent angles?
That gives us an isosceles triangle. Thus [imath]3x-2=2x+3[/imath] which [imath]\Rightarrow x=5[/imath]
From which we get the lengths of the sides: [imath]13\,, 13\ \&\ 25[/imath]
Then the answer to the question is immediate.
 
pka said:
What a frustrating thread! Did anyone else notice the red arcs which indicate congruent angles?
That gives us an isosceles triangle. Thus [imath]3x-2=2x+3[/imath] which [imath]\Rightarrow x=5[/imath]
From which we get the lengths of the sides: [imath]13\,, 13\ \&\ 25[/imath]
Then the answer to the question is immediate.
Click to expand...
Yes frustrating indeed - however, in post#4, the op displayed the solution .
 
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