Question

why is the pythagorean theorem important in real - world applications? a. it determines the color of objects b. it provides a method for calculating distances accurately c. it helps in measuring the volume of objects d. it is used to find the mass of objects the formula for the space diagonal of a rectangular prism is: a. $sqrt{l^{2}-w^{2}-h^{2}}$ b. $l^{2}+w^{2}+h^{2}$ c. $sqrt{l^{2}+w^{2}+h^{2}}$ d. $l + w + h$

Explanation:

1. The Pythagorean Theorem ($a^{2}+b^{2}=c^{2}$) is used to find the length of the sides of a right - triangle. In real - world applications, it can be used to calculate distances accurately. For example, in construction, navigation, etc. It has nothing to do with color, volume or mass.
2. For a rectangular prism with length $l$, width $w$ and height $h$, using the Pythagorean Theorem twice, we can derive the formula for the space diagonal $d=\sqrt{l^{2}+w^{2}+h^{2}}$.

Answer:

1. b. It provides a method for calculating distances accurately
2. c. $\sqrt{l^{2}+w^{2}+h^{2}}$