An open rectangular box with a volume of 12 cubic meters has a length that is 5 times the width. Express the surface area of the
1 answer:
The area of a 2D form is the amount of space within its perimeter. The surface area of the prism is 5x²+(24/5x)+(24/x).
<h3>What is an area?</h3>The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm2, m2, and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the rectangular box be x. Therefore, the length of the box is 5x. Now, the height of the box can be written as,
Volume of the box = length × width × Height
12 = 5x² × H
H= 12 / 5x²
Further, the surface area of the open box is,
Surface area of the box
Hence, the surface area of the prism is 5x²+(24/5x)+(24/x).
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Answer:
The original duration of the tour = 20 days
Step-by-step explanation:
Solution:
Total expenses for the tour = $360
Let the original tour duration be for days.
So, for days the total expense = $360
<em>Thus the daily expense in dollars can be given by</em> =
Tour extension and effect on daily expenses.
The tour is extended by 4 days.
<em>Tour duration now</em> = days
On extension, his daily expense is cut by $3
<em>New daily expense in dollars </em>=
Total expense in dollars can now be given as:
Simplifying by using distribution (FOIL).
We know total expense remains the same which is = $360.
So, we have the equation as:
Multiplying each term with to remove fractions.
Subtracting both sides
Dividing each term with -3.
Adding both sides.
Solving using quadratic formula.
For a quadratic equation:
Plugging in values from the equation we got.
So, we have
and
and
∴ and
Since number of days cannot be negative, so we take as the solution for the equation.
Thus, the original duration of the tour = 20 days