If sides of a right angled traingle are in A.P. , then sides are proportional to

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8. Sequences and Series

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

A

$1:2:3$

B

$2:3:4$

C

$3:4:5$

D

$4:5:6$

Solution

(c) Let the sides of the triangle be $a – d,\;a,\;a + d$,

then hypotenuse being the greatest side $i.e.$ $a + d$.

So, ${(a + d)^2} = {a^2} + {(a – d)^2}$

$ \Rightarrow $ ${a^2} + {d^2} + 2ad = {a^2} + {a^2} – 2ad + {d^2} $

$\Rightarrow a = 4d$

Therefore ratio of the side $s = a – d:a:a + d$

$ = (4d – d)\;:\;4d:(4d + d) = 3:4:5$.

Standard 11

Mathematics

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