A quilt maker is creating a design of a sailboat. she needs exactly the same amount of fabric for the sail as she needs for the body of the boat if the length of the bottom of the sail is equal to the short base of the boat what is the length of the long base of the trapezoid
A. 5
B. 10
C. 15
D. 25
Let's denote the length of the short base of the boat as "x." According to the given information, the length of the bottom of the sail is also "x."
A trapezoid has two bases: a short base and a long base. Since the short bases of the boat and the sail are the same, we can conclude that the short base of the boat is also equal to the short base of the trapezoid, which is "x."
Now, let's denote the length of the long base of the trapezoid as "y." Since the quilt maker needs exactly the same amount of fabric for the sail as she needs for the body of the boat, the area of the sail is equal to the area of the boat. The area of a trapezoid can be calculated using the formula:
Area = (1/2) * (sum of the bases) * (height)
The height of the trapezoid is the same as the height of the sail, which is the same as the height of the boat. Since these are not given in the question, we can assume they are equal and denote the height as "h."
So, the area of the sail is (1/2) * (x + y) * h, and the area of the boat is (1/2) * x * h.
Since these two areas are equal, we can write the equation:
(1/2) * (x + y) * h = (1/2) * x * h
Dividing both sides of the equation by (1/2) * h gives:
x + y = x
Subtracting x from both sides gives:
y = 0
Since y = 0, the length of the long base of the trapezoid is 0.
Therefore, based on the given information, none of the options A (5), B (10), C (15), or D (25) are correct.
To solve this problem, we need to understand the relationship between the sail and the body of the boat.
Let's say the length of the short base of the boat is "x". According to the problem, the length of the bottom of the sail is equal to the short base of the boat, which means it is also "x".
Now, we need to find the length of the long base of the trapezoid. Since the sail and the body of the boat need exactly the same amount of fabric, the length of the long base of the trapezoid should also be equal to "x".
Therefore, the length of the long base of the trapezoid is "x".
However, in the answer choices, we have values instead of variables. To find the specific value for the length, we need more information or context provided in the problem. Without any additional information, we cannot determine the exact value for the length of the long base of the trapezoid.
Thus, the answer cannot be determined with the given information.
Or...
Set the area of the triangle = area of the trapezoid
Then
re-arrange for "the missing length"
And you will have your formula for the length of the long side : )