SOLUTION: A square plot of land has a building 80 ft long and 40 ft wide at one corner. The rest of the land outside the building forms a parking lot. If the parking lot has area 8,900 ft2,

Algebra ->  Equations -> SOLUTION: A square plot of land has a building 80 ft long and 40 ft wide at one corner. The rest of the land outside the building forms a parking lot. If the parking lot has area 8,900 ft2,       Log On


   

Question 1152108: A square plot of land has a building 80 ft long and 40 ft wide at one corner. The rest of the land outside the building forms a parking lot. If the parking lot has area 8,900 ft2, what are the dimensions of the entire plot of land?
Found 3 solutions by greenestamps, MathLover1, ikleyn:
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


The building area is 80*40 = 3200 square feet; the parking lot is 8900 square feet.

Add the two areas to get the total; then find the dimensions of the plot of land, knowing that it is square.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A square plot of land has a building 80ft long and 40ft wide at one corner.
a building is80ft long and 40ft=>A=80ft%2A40ft=>A%5B1%5D=3200ft%5E2
The rest of the land outside the building forms a parking lot.
If the parking lot has area A%5B2%5D=8900ft%5E2, what are the dimensions of the entire plot of land?
given that plot is square, the length and width are same: a
total area of a square plot is : a%5E2 and it is = area of a building + area of a parking lot
a%5E2=A%5B1%5D%2BA%5B2%5D
a%5E2=3200ft%5E2%2B8900ft%5E2
a%5E2=12100ft%5E2
a=sqrt%2812100ft%5E2%29
a=110ft

then parking lot have dimensions:
a-40=110-40=70
and a-80=110-80=30


A%5B2%5D=8900ft%5E2
70%2A80%2B110%2A30=8900ft%5E2
5600%2B3300=8900ft%5E2

Answer by ikleyn(52864) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let the side length of the square plot of land be s feet.


Then its area is s^2 square feet.


The area of the house is 80*40 = 3200 square feet.


You are given  


    s^2 = 80*40 + 8900 = 12100  square feet


Hence,  s = sqrt%2812100%29 = 110 feet.    ANSWER

Solved.