SOLUTION: Please help me solve this equation: a playground is 25m x 40m. it is surrounded by a paved skating path of uniform width. the combined area of the playground and path is 1,426 squa

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Please help me solve this equation: a playground is 25m x 40m. it is surrounded by a paved skating path of uniform width. the combined area of the playground and path is 1,426 squa      Log On


   

Question 130616This question is from textbook
: Please help me solve this equation: a playground is 25m x 40m. it is surrounded by a paved skating path of uniform width. the combined area of the playground and path is 1,426 square meters. how wide is the path? This question is from textbook

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!

The area of the path is (draw the sketch):
2*x*(40+2x)+2*25*x simplifying
80x+4x^2+50x and this equals
4x^2+130x------------Area of the path
Area of the playground=40*25=1000 sq m
Area of the path=1426-1000=426 sq m
So----4x^2+130x=426 subtract 426 from both sides
4x^2+130x-426=0 divide each term by 2
2x^2+65x-213=0 ----------------quadratic in standard form--solve using the quadratic formula
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-65+%2B-+sqrt%28+65%5E2-4%2A2%2A%28-213%29+%29%29%2F%282%2A2%29+
x+=+%28-65+%2B-+77%29%2F%284%29+
Disregard the negative value for x; in this case, lengths are positive
So:
x=12%2F4=3 ft-----------------width of the path
CK
(25+6)(40+6)=1426
31*46=1426
1426=1426
Hope this helps---ptaylor