Question

how many different triangles of same area can be drawn without changing the lengths of two sides? ​

Answer 1

not a single triangle of same area can be drawn without changing the lengths of two sides. it means zero (0)

Answer 2

Concept :

In geometry, a triangle is a three-sided polygon made up of three vertices. These vertices are connected end-to-end at a point, which forms the triangle's angles. The sum of all three angles equals 180 degrees.

Given :

Different triangles of same area can be drawn without changing the lengths of two sides.

Find :

how many different triangles of same area can be drawn without changing the lengths of two sides.

Solution :

• more or less. The area of a triangle may be determined from two sides and the included angle:

K = ½*a*b*sin(C)

Generally two values of C, one acute, one obtuse will satisfy this. There is an exception of an unique solution if C happens to be 90°, (or π/2 radians). Also, if K > ½*a*b, there is no solution.

Hence The area of a triangle may be determined from two sides and the included angle.

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