Question

Bob takes a shortcut along the diagonal of a rectangular plot that is 32 cm wide and 24 cm long, instead of going along the sides. How much does that shorten his path?

a) 20 cm
b) 28 cm
c) 36 cm
d) 40 cm

Answer 1

Bob's path is shortened by 40 cm.

Step-by-step explanation:

To find how much Bob's path is shortened, we need to compare the length of the shortcut he takes along the diagonal of the rectangular plot to the sum of the lengths of the two sides he would have walked if he went along the sides. The Pythagorean theorem can be used to calculate the length of the diagonal (hypotenuse). In this case, the diagonal is the square root of the sum of the squares of the width and length of the rectangle, which is √(32² + 24²) = √(1024 + 576) = √(1600) = 40 cm. Therefore, Bob's path is shortened by 40 cm.