Find-the-total-number-of-integral-sided-triangle-whose-largest-side-is-30-please-explain-with-workings-

Question Number 44142 by Tawa1 last updated on 22/Sep/18

Find the total number of integral sided triangle whose largest side

is 30 .

please explain with workings

Answered by MrW3 last updated on 22/Sep/18

{l e t}^{'} s s a y t h e l a r g e s t s i d e i s c w i t h

c = 30

a + b > c, a ⩽ b < 30

w i t h b = 29 : a = 2, 3, \dots, 29 \Rightarrow 28 t r i a n g l e s

w i t h b = 28 : a = 3, 4 \dots, 28 \Rightarrow 26 t r i a n g l e s

w i t h b = 27 : a = 4, 5, \dots, 27 \Rightarrow 24 t r i a n g l e s

\dots \dots

w i t h b = 16 : a = 15, 16 \Rightarrow 2 t r i a n g l e s

t o t a l n u m b e r o f p o s s i b l e t r i a n g l e s :

2 + 4 + \dots + 24 + 26 + 28 = 2 (1 + 2 + \dots + 14)

= 2 \times \frac{14 \times (1 + 14)}{2} = 14 \times 15 = 210

Commented by Tawa1 last updated on 22/Sep/18

God bless you sir . I really appreciate

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