Answered

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what is the dimension of the rectangular box if the volume is 64 ft^{3} and if the width is 3 times longer than the height, and length is 9 times longer than the height??

Sagot :

Volume of rectangle = Length x Width x Height

Let height be x
Width be 3x
Length be 9x
Volume = 64 ft³

(x) (3x) (9x) = 64

27x³ = 64

[tex] \sqrt[3]{27x ^{3} } = \sqrt[3]{64} [/tex]

3x = 4

3x/3 = 4/3

x = 4/3 ft.

The dimensions are:
Height: x = 4/3 ft
Width: 3x = 3(4/3)  = 4 ft
Length: 9x = 9 (4/3) = 12 ft

To check:

(4/3 ft) (4 ft) (12 ft) = 65 ft³

(4/3 ft) ( 48 ft²) = 64 ft³

64 ft³ = 64 ft³