Mary walks from comer D to comer E to comer F on a city block that measures 264 feet wide and 900 feet long. Kate walks diagonally across the city block from comer D to comer F. How much less distance did Kate walk than Mary to get to comer
F? Round your answer to the nearest whole foot. Enter only the number.
D
900 feet
264 feet
The solution is

Difference between the distances traveled by Mary and Kate = 226 feet

Step-by-step explanation:

By applying Pythagoras theorem in right ΔDEF,

(DE)² + (EF)² = (DF)²

By substituting DE = 264 feet and EF = 900 feet

(264)² + (900)² = (DF)²

DF = √(69696+810000)

     = √879696

     = 937.92

Distance traveled by Kate diagonally = 938 feet

Distance traveled by Mary = DE + EF

                                            = 264 + 900

                                            = 1164 feet

Difference between the distances traveled by Mary and Kate = DF - (DE + EF)

= 1164 - 937.92

= 226.07

≈ 226 feet