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3 years ago

The dimensions of a carriage are:

Mathematics

1 answer:

jasenka [17]3 years ago

5 0

Answer:

Step-by-step explanation:

length * width * height = 1050 cubic ft

(10x + 5)* (2x -1) * (x +3) = 1050

(10x + 5 )(2x-1) = 10x*(2x - 1) + 5*(2x -1)

= 10x*2x - 10x*1 + 5*2x - 1*5

= 20x² - 10x + 10x - 5 = 20x² - 5

(10x + 5)(2x -1)(x+3) = (20x² -5) *(x + 3)

=20x²*(x +3) - 5*(x +3)

= 20x³ + 60x² - 5x - 15

20x³ + 60x² - 5x - 15 = 1050

20x³ + 60x² - 5x - 15 - 1050 = 0

20x³ + 60x² - 5x - 1065 = 0

By trial and error method , (x -3 ) is a factor

Synthetic method:

3 ( 20 60 -5 -1065

( 60 360 1065

20 120 355 0

20x² + 120x + 355 = 0

Divide the equation by 5

4x² + 24x + 71 = 0 . Solving this equation gives imaginary number. So, ignore these values.

So, value of x = 3

height = 3+ 3 = 6 ft

Length = 10*3 + 5 = 30 + 5 = 35ft

Width = 2x - 1 = 2*3 - 1 = 6 - 1 = 5 ft

Check: length * width * height = 35 * 5 * 6 = 1050 cubic ft

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