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 Si\displaystyle S_i be the length of one triangle leg, then the perimeter of the triangle is:

S1+S2+S3=3x−2+2x+3+5x=10x+1\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 x\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

3x−2=2x+3\displaystyle 3x - 2 = 2x + 3
3x−2x=3+2\displaystyle 3x - 2x = 3 + 2
x=5\displaystyle x = 5

This means that the perimeter of the triangle is 10x+1=10(5)+1=50+1=51\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 3x−2=2x+33x-2=2x+3 which ⇒x=5\Rightarrow x=5
From which we get the lengths of the sides: 13 ,13 & 2513\,, 13\ \&\ 25
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 3x−2=2x+33x-2=2x+3 which ⇒x=5\Rightarrow x=5
From which we get the lengths of the sides: 13 ,13 & 2513\,, 13\ \&\ 25
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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