Triangle ABC has integral sides measuring 2001 units and 1002 units repectively The no of such triangles is - Maths - Triangles

Question

Triangle ABC has integral sides measuring 2001 units and 1002 units
repectively The no of such triangles is??

Varun.Rawat · Accepted Answer

We have ABC as the given ∆ Let AB = 2001 units ; BC = 1002 unitsWe know that sum of any 2 sides of a triangle is always greater than third side So, AB + BC > CA⇒2001 + 1002 > CA⇒CA < 3003 unitsAlso, we know that, difference of any 2 sides of a triangle is always less than the third side So, AB - BC < CA⇒2001 - 1002 < CA⇒CA > 999Hence, 999 < CA < 3003Lowest integral value that CA can take is 1000 and highest integral value that CA can take is 3002 Total number of possible values of CA = 2003hence, possible number of such triangles = 2003

Triangle ABC has integral sides measuring 2001 units and 1002 units repectively. The no. of such triangles is??