Question

the length of a rectangle is 8cm more than the width and its area is 172cm2 .find the width of the rectabgle

Answer 1

`l-the\ length\\l+8-the\ width\\A=172\ cm^2\\\\A=lengtf\cdot width\\\\subtitute\\\\l(l+8)=172\\\\l^2+8l=172\ \ \ |subtract\ 172\ from\ both\ sides\\\\l^2+8l-172=0\\a=1;\ b=8;\ c=-172\\\\\Delta=b^2-4ac\\\\\Delta=8^2-4\cdot1\cdot(-172)=64+688=752 > 0\\\\l_1=(-b-\sqrt\Delta)/(2a)\ and\ l_2=(-b+\sqrt\Delta)/(2a)\\\\\sqrt\Delta=√(752)=√(16\cdot47)=4√(47)\\\\l_1=(-8-4√(47))/(2\cdot1)=-4-2√(47) < 0\\\\l_2=(-8+4√(47))/(2\cdot1)=-4+2√(47) > 0\\\\The\ width:l+8=-4+2√(47)+8=4+2√(47)\\\\Answer:\boxed{length=(2√(47)-4)cm;\ width=(4+2√(47))cm}`

`length\approx9.71cm;\ width\approx17.71cm`