Requesting hint for a problem

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I tried this problem many times, but couldn’t solve it :frowning:
It (PTS) can be an equilateral triangle, an isosceles triangle, or a scalene triangle. Which one is true?
At first, I tried with an equilateral triangle, I didn’t have to use any trigonometry in that case, only Pythagoras’ theorem. But the answer was wrong.
Then, I tried with an isosceles triangle with trigonometry. But that one was also incorrect.
At last, I tried with a scalene triangle. But I found that it’s not possible to determine the value of the perimeter of PTS if it’s a scalene triangle.

Can anyone please provide any hint?

Same problem with me😭

Here \triangle{PTS} can be an isosceles triangle, or a scalene triangle. But the perimeter of the triangle is always same. So to solve this problem, you have to take the triangle in such a way that you can easily find the value of its side. And it is the isosceles triangle.
I am giving you a hint. It is your choice that you see it or not.

It is a hint of this problem. if you don't want to deterioration of your math skill, then don't click it. (If you are not solve this problem yet)

The problem is very easy to solve when \triangle{PTS} is an isosceles triangle. You can solve the problem using similarities of all triangle.
সমস্যাটি সমাধান করা খুব সহজ যখন \triangle{PTS} একটি সমদ্বিবাহু ত্রিভুজ। এখানে ত্রিভুজের সদৃশতা ব্যবহার করে সমস্যার সমাধান করা যাবে।


Thanks for helping. It was really useful.

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