Chapter 9.3, Problem 20E

To determine

The distance that the carpenter measure

Answer to Problem 20E

Distance that carpenter measured is 5 inches.

Explanation of Solution

Given:

The length of mark carpenter made on one side of shelf = 3 inches

The length of mark carpenter made on second side of shelf = 4 inches

Calculation:

To find the distance that the carpenter measured to make sure that the corner is a right angle, we put the given values in Pythagoras Theorem:

  $\begin{array}{l}{c}^2=a^2+b^2\\ {\left(c\right)}^2={\left(3\right)}^2+{\left(4\right)}^2\\ {\left(c\right)}^2=9+16\\ {\left(c\right)}^2=25\\ c=\sqrt{25}\\ c=5inch\end{array}$

Hence, the distance that the carpenter measured is 5 inches

This method works because when we put the values of three sides in Pythagoras Theorem, it gives the same result on both sides. Pythagoras Theorem generates equal values on both the sides when the sides of the triangle are right angled.