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Question 79
The three sides of a right-angled triangle have integral lengths and also form an arithmetic progression. A possible length of one of the sides is
Solution
Let the three sides be $$(a-d),a,(a+d)$$ units
In a right angled triangle,
=> $$(a-d)^2+(a)^2=(a+d)^2$$
=> $$2a^2+d^2-2ad=a^2+d^2+2ad$$
=> $$a^2=4ad$$
=> $$a=4d$$
Thus, the three sides are : $$3d,4d,5d$$
Thus, the sides are multiples of either 3,4 or 5. Thus, only possible side among the options is 56.
=> Ans - (D)
