SOLUTION: A rectangular field has dimensions 70m long and 50m wide. The field has a x m border around it which is a rectangular concrete path. The area of the path which is shaded is 1024m^2

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: A rectangular field has dimensions 70m long and 50m wide. The field has a x m border around it which is a rectangular concrete path. The area of the path which is shaded is 1024m^2      Log On


   

Question 1113066: A rectangular field has dimensions 70m long and 50m wide. The field has a x m border around it which is a rectangular concrete path. The area of the path which is shaded is 1024m^2.
Found 2 solutions by ikleyn, josgarithmetic:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
The RULE of this forum is: 

    Each post must have a question.

    Posts without questions are the subject of ignoring.

===============

You even can not imagine how much do you lose when violate the rules !



Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Area of the field: 70%2A50 square meters

Area of field AND uniform widthed path: %282x%2B70%29%282x%2B50%29

Area of the surrounding path only: highlight_green%28%282x%2B70%29%282x%2B50%29-70%2A50=1024%29

Solve for x, the width of the concrete path around the field.
-
4x%5E2%2B140x%2B100x%2B70%2A50=1024
4x%5E2%2B240x=1024
x%5E2%2B60x-256=0
%28x-4%29%28x%2B64%29=0
highlight%28x=4%29-------the width of the uniform path