Question 706433
the length here: H+12
the with would be: H-3
and the hight is just: H
.
(H)*(H-3)*(H+12)=324
now, we FOIL:
(H)*(H^2+9H-36)=324
H^3+9H^2-36H=324
H^3+9H^2-36H-324 = 0
then, we group:
(H^3+9H^2)-(36H+324) = 0
H^2(H+9)-36(H+9) = 0
(H+9)(H^2-36) = 0
H = {-9, -6, 6}
Throw out the negative solutions (extraneous) leaving:
H = 6 feet (height)
.
width:
H-3 = 6-3 = 3 feet
.
length:
H+12 = 6+12 = 18 feet