​​​in triangle ABC  angle B =90 degree . find the sides of the triangle , if AB= (x-3) ,AC =(x+6) , BC=(x +4)

 

Dear student,

In rt angled ABC,By Pythagoras theoremAC2=AB2+BC2x+62=x-32+x+42x2+36+12x=x2+9-6x+x2+16+8x           ...[using (a±b)2=a2+b2±2ab]36-9-16+12x+6x-8x=x2+x2-x236-9-16+12x+6x-8x=x211+10x=x2x2-10x-11=0x2-11x+x-11=0xx-11+1x-11=0x-11x+1=0x=11 or x=-1When x=-1AB=x-3=-1-3=-4thus neglecting x=-1 as length cannot be negativeSo, when x=11AB=x-3=11-3=8AC=x+6=11+6=17BC=x+4=11+4=15

Regards

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i think so the sides are 2 , 11, 9
if you want explanation let me no
 
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