9. The length and width of the rectangular bottom of Sabrina's new fish tank is twice the length and width of the rectangular bottom of her old tank. The area of the bottom of the new tank is 16 ft^2. The lengh of the old tank was 3 feet more than the width of the new tank.
a. Using F to represent the width of the old tank, write an equation to show the area of the new tank bottom
ok so F=old width y=old legnth z=new width x=new legnth
we have 2F=z 2y=x
and area=16=lw=xz and y=3+z
subsitute 3+z for y 2(3+z)=6+2z=x subsitute 6+2z for x in xz=16 (6+2z)(z)=16 solve for z distribute 2z^2+6z=16 divide 2 z^2+3z=8 subtract 8 z^2+3z-8=0 solve using quadratic formula z=1.7 subsitute zx=16 1.7*x=16 divide booth sides by 1.7 x=9.41 legnth(new)=9.41 ok so we know that doubleold=new so old=1/2new 1.7=newW oldW=1.7/2=0.85
so equatn is (6+2z)(z)=16 z=width b. width of old tank=0.85 c. legnth of new=9.41
