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