Question 92
ΔPQR has sides PQ and PR measuring 983 and 893 units respectively. How many such triangles are possible with all integral sides?
Solution
Let us assume that the length of the third side is x units.
Case 1: When the side PQ is the largest among three sides.
893 + x > 983
x > 90
Case 2: When the side QR is the largest among the three sides.
893 + 983 > x
x < 1876
Hence we can say that x $$\epsilon$$ (90, 1876)
Hence, the number of with integral value = 1875 - 91 +1 = 1785.
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