suppose a spider was able to create one threat that would extend from the top right back corner of its tank the bottom left front corner. Approximately how long would that thread need to be for the tank below? (The height is 24, width is 10, and length is 32) (Shape is a rectangular prism). Round your answer to the nearest tenth.
The diagonal of the bottom of the tank is (to the nearest tenth of an inch (___) inches.
To the nearest tenth of an inch, the length of the spiders thread is ___ inches
To find the length of the diagonal of the bottom of the tank, we can use the Pythagorean theorem. Let's label the dimensions of the tank as follows:
Length (L) = 32
Width (W) = 10
Height (H) = 24
The diagonal of the bottom can be found by considering the diagonal of the rectangle formed by the length and width. This diagonal can be seen as the hypotenuse of a right triangle with the length and width as its legs.
Using the Pythagorean theorem, we have:
Diagonal^2 = Length^2 + Width^2
Diagonal^2 = 32^2 + 10^2
Diagonal^2 = 1024 + 100
Diagonal^2 = 1124
Taking the square root of both sides, we get:
Diagonal = sqrt(1124)
Diagonal ≈ 33.5 inches (rounded to the nearest tenth)
Therefore, the length of the spider's thread would need to be approximately 33.5 inches to extend from the top right back corner to the bottom left front corner of the tank.