Question

Δpqr has sides pq and pr measuring 983 and 893 units respectively. How many such triangles are possible with all integral sides?

Answer 1

In ABC:

AB = 10 | BC = 15 | AC = x

Using property:1

10+15 > x | 25 > x | x < 25

15 + x > 10 | x > - 5 | x > 0

10 + x > 15 | x > 5 | 5 < x

Combining we get: 5 < x < 25

Integral values of x = 6, 7, 8, 9, 10, ….., 24 = 19 values

Using Property 2:

15 - 10 < x | 5 < x

x - 15 < 10 | x < 25

10 - x < 15 | - 5 < x | x > - 5 | x > 0

Combining we get: 5 < x < 25

Integral values of x = 6, 7, 8, 9, 10, ….., 24 = 19 values