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if ratio is 1:2:1
let the angle is x,2x,x
sum of angle is 180 then
x+2x+x =180
4x =180
x =45 is isoscale triangle two side are equel
right angle at R so PR is base PQ is hypotenuse
so
PQ^2= PR^2 +QR^2
= 2 PR^2
=2*4*3
PQ =2√6
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