how long is the diagonal of a 12mm-by-16mm face of a rectangular prism?
Use Pythagoras theorem:
Diagonal = sqrt(12²+16²)
= sqrt(144+256)
= sqrt(400)
= 20
Why did the rectangular prism go to the dentist? Because it had a diagonal ache!
Now, to answer your question, we can use the Pythagorean theorem to find the length of the diagonal. The theorem states that the square of the length of the diagonal is equal to the sum of the squares of the other two sides.
So, let's calculate it:
Length^2 + Width^2 = Diagonal^2
(12mm)^2 + (16mm)^2 = Diagonal^2
144mm + 256mm = Diagonal^2
400mm = Diagonal^2
Taking the square root of both sides, we have:
Diagonal = √400mm
Diagonal = 20mm
So, the diagonal of the 12mm-by-16mm face of the rectangular prism is 20mm.
To find the length of the diagonal of a 12mm-by-16mm face of a rectangular prism, you can use the Pythagorean theorem.
The Pythagorean theorem states that for a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
So, the diagonal is the hypotenuse of a right triangle formed by the two sides of the rectangular face.
Let's label the sides of the face as follows:
Length (L) = 16mm
Width (W) = 12mm
Using the Pythagorean theorem:
Diagonal (D)^2 = Length (L)^2 + Width (W)^2
Substituting the values:
D^2 = 16^2 + 12^2
D^2 = 256 + 144
D^2 = 400
Taking the square root of both sides to find the length of the diagonal:
D = √400
D = 20mm
Therefore, the length of the diagonal of the 12mm-by-16mm face of the rectangular prism is 20mm.
To find the length of the diagonal of a face of a rectangular prism, you can use the Pythagorean theorem.
The Pythagorean theorem 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 diagonal across the face of the rectangular prism forms a right triangle with the sides measuring 12mm and 16mm.
Let's call the length of the diagonal "d". Applying the Pythagorean theorem, we have:
d² = 12² + 16²
d² = 144 + 256
d² = 400
Taking the square root of both sides, we find:
d ≈ √400
d ≈ 20 mm
Therefore, the length of the diagonal of the 12mm-by-16mm face of the rectangular prism is approximately 20mm.