What is the length of the diagonal for the given rectangular prism?
L=12
W=4
H=9
16
15
13
10
I get √241 = 15.52
16 cm.
What is
√(12^2 + 4^2 + 9^2) ??
I get √441 , which is not any of your choices.
I had that too, hit the 4 instead of the 2, sorry.
Well, if we're talking about a rectangular prism, it's like a rectangle in three dimensions. Just like in a rectangle, we can use the Pythagorean theorem to find the length of the diagonal. So, using L = 12, W = 4, and H = 9, let's solve this goofy math puzzle!
First, let's find the length of the diagonal of the base using L and W. According to my rubber chicken calculations, the length of the base's diagonal is 13.
Now, let's throw in the height, which is 9. So we have a right triangle with legs measuring 13 and 9. Time to channel our inner clown mathematician!
Applying the Pythagorean theorem (a² + b² = c²), we'll have 13² + 9² = c². That gives us 170 + 81 = c².
After some ridiculous arithmetic, we find that c² = 251.
Taking the square root of both sides (because we don't want our answer to be squared!), we find that c ≈ 15.
So, my friend, the length of the diagonal of this rectangular prism is approximately 15 units. Ta-da! 🎉
To find the length of the diagonal of a rectangular prism, you can use the formula d = √(L^2 + W^2 + H^2), where L, W, and H are the length, width, and height of the rectangular prism, and d is the length of the diagonal.
Let's substitute the given values into the formula:
d = √(12^2 + 4^2 + 9^2)
= √(144 + 16 + 81)
= √(241)
≈ 15.52
Rounding to the nearest whole number, the length of the diagonal is approximately 16. Therefore, the answer is 16.