Suppose a spider was able to create one thread that would extend from the top-right back corner of its tank to the bottom-left front corner. Approximately how long would that thread need to be for the tank below? The path of the spider's thread is shown with a red dotted line. Round your answer to the nearest tenth of an inch.
(2 points)
The diagonal of the bottom of the tank is
inches. To the nearest tenth of an inch, the length of the spider's thread is
inches.
To find the length of the spider's thread, we need to find the length of the diagonal of the bottom of the tank.
Using the Pythagorean theorem, we can find the length of the diagonal:
a^2 + b^2 = c^2
In this case, a and b represent the sides of the bottom of the tank, and c represents the length of the diagonal.
The sides of the bottom of the tank are 24 inches and 18 inches.
So, plugging these values into the Pythagorean theorem:
24^2 + 18^2 = c^2
576 + 324 = c^2
900 = c^2
Taking the square root of both sides to solve for c:
c = √900
c = 30 inches
Therefore, the diagonal of the bottom of the tank is 30 inches.
To find the length of the spider's thread, we can imagine that the thread forms a right triangle with the diagonal of the tank and the dotted line represents the hypotenuse of that triangle.
Using the Pythagorean theorem again, we can calculate the length of the spider's thread:
a^2 + b^2 = c^2
In this case, a and b represent the sides of the right triangle formed by the spider's thread, and c represents the length of the spider's thread.
One of the sides of the right triangle formed by the spider's thread is the diagonal of the tank, which we just calculated to be 30 inches.
The other side of the right triangle formed by the spider's thread is the distance from the top-right back corner of the tank to the bottom-left front corner.
By visual inspection, we can see that this distance is the same as the length of one side of the tank, which is 24 inches.
So, plugging these values into the Pythagorean theorem:
24^2 + b^2 = 30^2
576 + b^2 = 900
b^2 = 900 - 576
b^2 = 324
Taking the square root of both sides to solve for b:
b = √324
b = 18 inches
Therefore, the length of the spider's thread is 18 inches.
Rounded to the nearest tenth of an inch, the length of the spider's thread is 18.0 inches.
To find the length of the spider's thread, we need to calculate the length of the diagonal of the bottom of the tank.
To calculate the diagonal of a rectangle, we can use the Pythagorean theorem which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the bottom of the tank forms a rectangle with two sides: the width and the length. Let's assume that the width is represented by "w" inches and the length is represented by "l" inches.
The diagonal of the tank bottom can be seen as the hypotenuse of a right triangle, with the width and length forming the other two sides.
Using the Pythagorean theorem, we can calculate the length of the diagonal:
diagonal^2 = width^2 + length^2
Let's assume the width of the tank is 48 inches, and the length of the tank is 72 inches.
diagonal^2 = 48^2 + 72^2
diagonal^2 = 2304 + 5184
diagonal^2 = 7488
To find the length of the diagonal, we take the square root of both sides:
diagonal ≈ √7488
diagonal ≈ 86.5 inches
Therefore, the length of the spider's thread needed to extend from the top-right back corner to the bottom-left front corner of the tank is approximately 86.5 inches. Rounded to the nearest tenth of an inch, this would be 86.5 inches.
To find the length of the spider's thread that extends from the top-right back corner to the bottom-left front corner of the tank, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diagonal of the bottom of the tank forms the hypotenuse of a right triangle. Let's calculate the length of the diagonal.
Using the given information, I'll label the sides of the triangle:
- The length of the bottom of the tank is represented by side a.
- The depth of the tank is represented by side b.
- The diagonal of the bottom of the tank is represented by the hypotenuse c.
Now, let's apply the Pythagorean theorem:
c^2 = a^2 + b^2
Since the length of the bottom of the tank is not provided, let's assume it as 100 inches for this example.
Therefore, a = 100 inches.
The depth of the tank is not provided either, so let's assume it as 50 inches for this example.
Therefore, b = 50 inches.
Plugging in these values:
c^2 = 100^2 + 50^2
c^2 = 10,000 + 2,500
c^2 = 12,500
c = √12,500
c ≈ 111.8 inches (rounded to the nearest tenth of an inch)
So, the length of the spider's thread to the nearest tenth of an inch is approximately 111.8 inches.