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.
12in 35in 16in
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 diagonal of the bottom of the tank, we can use the Pythagorean theorem. The two sides of the tank forming the bottom are 12in and 35in.
Using the Pythagorean theorem, we can calculate the length of the diagonal:
diagonal^2 = 12^2 + 35^2
diagonal^2 = 144 + 1225
diagonal^2 = 1369
diagonal = √1369
diagonal ≈ 37in (rounded to the nearest whole inch)
The length of the spider's thread would need to be approximately equal to the length of the tank's diagonal, which is approximately 37in. We round this to the nearest tenth of an inch, which gives us 37.0in.
To find the length of the spider's thread, we can use the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle 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, with the two sides being 12 inches and 35 inches.
Using the Pythagorean theorem:
(diagonal)^2 = (12)^2 + (35)^2
(diagonal)^2 = 144 + 1225
(diagonal)^2 = 1369
Taking the square root of both sides to solve for the diagonal:
diagonal = square root of 1369
diagonal ≈ 36.9 inches
Therefore, the length of the spider's thread would need to be approximately 36.9 inches when rounded to the nearest tenth of an inch.
To find the length of the diagonal of the bottom of the tank, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (diagonal) is equal to the sum of the squares of the other two sides.
In this case, the other two sides are the length of the tank (12 inches) and the width of the tank (35 inches).
So, using the Pythagorean theorem: diagonal^2 = 12^2 + 35^2
diagonal^2 = 144 + 1225
diagonal^2 = 1369
Taking the square root of both sides:
diagonal = √1369
diagonal ≈ 36.98 inches
Rounded to the nearest tenth of an inch, the length of the diagonal of the tank bottom is approximately 37.0 inches.
Now, since the spider's thread has to extend from the top-right back corner to the bottom-left front corner, its length is equal to the length of the diagonal of the bottom of the tank. So, to the nearest tenth of an inch, the length of the spider's thread is approximately 37.0 inches.