Question

use the image to answer the question.(2 points)first, we will use side lengths $\boldsymbol{square}$ in the pythagorean theorem to find the diagonal length of the base rectangle. second, we will use 12 and the length we found in step one to solve for the diagonal of the prism. the length of the diagonal of the prism is $\boldsymbol{square}$.hint: dont forget to use your desmos calculator and staar reference sheet to help!

Explanation:

Step1: Identify base side lengths

Base sides: $3$ cm, $4$ cm

Step2: Calculate base diagonal

Use Pythagorean theorem:
$$d_{base} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ cm}$$

Step3: Calculate prism diagonal

Use height $12$ cm and base diagonal:
$$d_{prism} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ cm}$$

Answer:

First blank: 3 cm and 4 cm
Second blank: 13 cm