Esther starts at one corner of a square field and walks 90 feet along one side to another corner of the field. she turns 90° and walks 70 feet, and then walks straight back to where she started. what is the area of the part of the field she walked around?
a. 3150 ft²
b. 4900 ft²
c. 6300 ft²
d. 8100 ft²

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.