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. 32in 24in 10in
To find the length of the spider's thread, we need to use the Pythagorean theorem, which 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 tank can be viewed as a right triangle, where the two sides are 32 inches and 24 inches. So, we can use the Pythagorean theorem to find the length of the hypotenuse (the spider's thread).
The equation would be:
hypotenuse^2 = 32^2 + 24^2
Simplifying the equation:
hypotenuse^2 = 1024 + 576
hypotenuse^2 = 1600
Taking the square root of both sides:
hypotenuse ≈ √1600
hypotenuse ≈ 40
Therefore, the length of the spider's thread would need to be approximately 40 inches.
But what is the diagonal of the bottom of the tank
To find the diagonal of the bottom of the tank, we can use the Pythagorean theorem again. The bottom of the tank forms a rectangle, and the diagonal is the hypotenuse of a right triangle within this rectangle.
The length of one side of the rectangle is 32 inches, and the width is 24 inches.
Using the Pythagorean theorem:
diagonal^2 = 32^2 + 24^2
Simplifying the equation:
diagonal^2 = 1024 + 576
diagonal^2 = 1600
Taking the square root of both sides:
diagonal ≈ √1600
diagonal ≈ 40
Therefore, the diagonal of the bottom of the tank is approximately 40 inches.