1.

The sides of a right angled triangle are inarithmetic progression. If the triangle has area 24, then what is the lengthof its smallest side?

Answer» a-d,a,a+d are in AP
`(a+d)^2=a^2+(a-d)^2`
`a^2+d^2+2ad=a^2+a^2-2ad+d^2`
`a^2-2ad-2ad=0`
`a^2-4ad=0`
`a(a-4d)=0`
`a-4d=0`
`a=4d`
`a!=0`
So, base=4d,perpendicular=3d,hypotenuse=5d
`1/2*b*h=1/2*4d*3d`
`6d^2=24`
`d^2=4`
`d=pm2`
d can not be negative
So, b=8,p=6,h=10.


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