Question

A triangular frame has three equal sides, $AB=BC=CD$. If the length of all the three given sides are halved, how many such triangles are possible?

• A. Infinitely many triangles, as there are infinite equilateral triangles possible.
  
• B. Unique triangle, as the triangle formed will also be an isosceles triangle.
• C. No triangle, as per the triangle inequality theorem.
• D. Unique triangle, as the triangle formed will also be an equilateral triangle

Answer 1

The correct option is D Unique triangle, as the triangle formed will also be an equilateral triangle

If the sides of the triangle are equal, then it is an equilateral triangle.
Even if we half every side, then also it remains an equilateral triangle.
For an equilateral triangle with the given sides, the result after halving the sides of a triangle will result in only one equilateral triangle of side
$\frac{AB}{2}=\frac{BC}{2}=\frac{CD}{2}$.

Example:


An equilateral triangle of side length $12\text{ft}$ when reduced to half also forms an equilateral triangle. In any equilateral triangle, all the three angles are ${60}^{\circ }$. So for the given triangle, there will be unique triangles that can be formed.

So, the correct answer is option B