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(C) Let the sides of the triangle be $(a - d)$,$a$,and $(a + d)$,where $d > 0$.Since the triangle is right-angled,the hypotenuse is the longest side,w

Vedclass · Accepted Answer

$3:4:5$

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(C) Let the sides of the triangle be $(a - d)$,$a$,and $(a + d)$,where $d > 0$.Since the triangle is right-angled,the hypotenuse is the longest side,which is $(a + d)$.According to the Pythagorean theorem,the square of the hypotenuse is equal to the sum of the squares of the other two sides:$(a + d)^2 = a^2 + (a - d)^2$Expanding both sides:$a^2 + d^2 + 2ad = a^2 + a^2 - 2ad + d^2$Simplifying the equation:$2ad = a^2 - 2ad$$a^2 - 4ad = 0$$a(a - 4d) = 0$Since $a$ represents a side length,$a 
eq 0$,so $a = 4d$.Substituting $a = 4d$ into the sides $(a - d, a, a + d)$:$(4d - d) : 4d : (4d + d) = 3d : 4d : 5d = 3:4:5$.

If the sides of a right-angled triangle are in $A.P.$,then the sides are proportional to

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