On moving day, Guyton needs to rent a truck. The length of the cargo space is , and the height is less than the width. The brochure indicates that the truck can hold . What are the dimensions of the cargo space

On moving day, Guyton needs to rent a truck. The length of the cargo space is 10 ft , and the height is 1 ft less than the width. The brochure indicates that the truck can hold 420 ft3 . What are the dimensions of the cargo space? Assume that the cargo space is rectangular shape.

The dimensions; width w is 7 ft and height is 6 ft

Step-by-step explanation:

L = 10 ft the length of the cargo space

w = the width of the cargo space

h = the height of the cargo space the height is 1 ft less than the width

h = w - 1

The truck can hold 420 ft^3 - this means the volume of the space V = 420 ft^3

But V = L*w*h

Substitute h = w - 1 into the Volume equation

Therefore,

10*w*(w - 1) = 420

10w^2 - 10w - 420 = 0

By Using quadratic equation formula to solve and considering positive answer,

w = {-b +- √(b^2 - 4ac)}/2a

Where;

a = 10, b = -10 and c = -420

w = {-(-10) +- √(-10^2 - 4(10)(-420)}/2(10)

w = {-(-10) +- 130}/20

w = (10 + 130)/20 = 140/20 = 7

Or

w = (10 -130)/20 = -120/20 = -6

Here,

I take positive answers and the width is 7 ft

Also, from h = w - 1

height = 7 - 1 = 6 ft

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