Answer:
width = 9 inches
length = 16 inches
height = 5 inches
Step-by-step explanation:
let x be with
x + 7 be length, because it's 7 inches longer than its width
x - 4 be height, because it's 4 inches less than the width
V = lwh , where V= 720 cubic inches
720 = (x + 7) (x) (x - 4)
720 = (x² + 7x)(x - 4)
720 = x³ + - 4x² + 7x² - 28x
720 = x³ + 3x² - 28x
x³ + 3x² - 28x - 720 = 0
(x - 9) (x²+ 12x + 80) = 0 , choose (x - 9) because it is the one that will give positive answer for x, because as for (x²+ 12x + 80) it will give two negative roots because the linear and constant terms were positive. As we know when we're talking about dimensions it must be positive.
equate x - 9 to zero
x - 9 = 0
x -9 + 9 = 0 + 9
x = 9, this is the width (9 inches)
length: x + 7 = (9) + 7 = 16 inches
height: x - 4 = (9) - 4 = 5 inches
