If the sides of a right-angled triangle are i | vedclass

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(C) Let the sides of the triangle be $a - d, a, a + d$,where $d > 0$.Since the hypotenuse is the longest side,it must be $a + d$.According to the Pyth

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$3:4:5$

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(C) Let the sides of the triangle be $a - d, a, a + d$,where $d > 0$.Since the hypotenuse is the longest side,it must be $a + d$.According to the Pythagorean theorem,$(a + d)^2 = a^2 + (a - d)^2$.Expanding both sides,we get $a^2 + d^2 + 2ad = a^2 + a^2 - 2ad + d^2$.Simplifying,we get $2ad = a^2 - 2ad$,which implies $a^2 = 4ad$.Since $a$ is a side length $(a 
eq 0)$,we divide by $a$ to get $a = 4d$.Substituting $a = 4d$ into the sides,we get $(4d - d) : 4d : (4d + d) = 3d : 4d : 5d$.Thus,the ratio of the sides is $3:4:5$.

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

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