To find the diagonal of the rectangular base of the prism, we can use the Pythagorean Theorem.
- The lengths of the rectangle's base are given as 3 cm (front base) and 4 cm (side base).
Using the Pythagorean theorem:
\[ d^2 = a^2 + b^2 \]
where \(a = 3\) cm and \(b = 4\) cm, we calculate the diagonal \(d\):
\[ d^2 = 3^2 + 4^2 = 9 + 16 = 25 \]
\[ d = \sqrt{25} = 5 \text{ cm} \]
So, Blank 1 is referring to the side lengths used in the Pythagorean theorem, which are 3 and 4.
- Now, we will use the diagonal of the base (5 cm) and the height of the prism (12 cm) to find the diagonal of the prism using the Pythagorean theorem again.
The formula for the diagonal \(D\) of the prism now becomes:
\[ D^2 = d^2 + h^2 \]
where \(d = 5\) cm (the diagonal of the base) and \(h = 12\) cm (the height of the prism):
\[ D^2 = 5^2 + 12^2 = 25 + 144 = 169 \]
\[ D = \sqrt{169} = 13 \text{ cm} \]
So, Blank 2 for the diagonal of the prism is 13 cm.
Putting it all together:
- Blank 1: 3 and 4
- Blank 2: 13
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