Respuesta :
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.
Answer:
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
As per the question on a moving day, the Guyton is renting a truck and the length of his cargo the height of which is less than the width. The brochure indicates the trick that he can hold.
How much width and height does Guyton need in cargo space?
The dimension of the cargo will be based on the amount of capacity of the cargo and the amount of cargo that needs to be moved. On the day of the move, he rent a truck. The L of all cargo space is given as 10 feet, and that of height is 1 foot which is less than the width. This brochure tells us that the truck can hold 420 feet.
Find out more information about the length of the cargo space.
brainly.com/question/1170096.
