A square plot of land has a building 70 ft long and 50 ft wide at one corner?

Question

A square plot of land has a building 70 ft long and 50 ft wide at one corner. The rest of the land outside the building forms a parking lot. If the parking lot has area 19,000 ft2, what are the dimensions of the entire plot of land?

Answer 1

Area of entire plot of land 22500ft²

 

There are no constraints on the dimensions of the entire plot of land.

 

Take the square root of 22500 which is 150.  one can place the building in one corner of the plot and the parking lot would still be 19000ft².  There are infinitely many solutions to this problem.

Answer 2

Kennedy,

I cannot stress enough how helpful it is to draw a picture for these types of problems! It is tough to do in this editor, but I will try.

                   X

-------------------------------------

|                                   |

|                                   |

|                                   |

|   50                             |  X

|________                     |

|            |                      |

|            |                      |

|            |  70                 |

--------------------------------------

 

So the area of the land, length x width, is X².

The area of the building is 3500.

The parking lot is the difference between them.

 

X² - 3500 = 19000

X² = 22500

X = 150             Area = 22500