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A new bakery at Subic accept orders of decorations cake for special occasions. The customer once the volume of cake to be 720 cubic inches. The cake is in the shape of the rectangular solid. The client want the length to be 7 inches longer than its width and the height is 4 inches less than the width. What should be the dimension of the cake?​

Sagot :

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