SOLUTION: Your neighbors have just finished installing a new swimming pool at their home. The pool measures 15 feet by 20 feet. They would like to plant a strip of grass of uniform width aro

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Your neighbors have just finished installing a new swimming pool at their home. The pool measures 15 feet by 20 feet. They would like to plant a strip of grass of uniform width aro      Log On


   



Question 1079201: Your neighbors have just finished installing a new swimming pool at their home. The pool measures 15 feet by 20 feet. They would like to plant a strip of grass of uniform width around three sides of the pool, the two short sides and one of the longer sides.

a) Sketch a diagram of the pool and the strip of lawn, using x to represent the width of the uniform strip.
b) write an equation for the area, A, in terms of x that represents the lawn area around the pool.
c) Your neighbors have enough seed for 168 square feet of lawn. Write an equation that relates the quantity of seed to the area of the uniform strip of lawn.
d) Solve the equation in part c to determine the width of the uniform strip that can be seeded.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
With the strip included, the length of a short side is:
+2x+%2B+15+
With the strip included, the length of a long side is:
+2x+%2B+20+
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The area of the entire strip of grass is:
+A%5B1%5D+=+%28+2x+%2B+15+%29%2A%28+2x+%2B+20+%29+-+15%2A20+
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Now I have to subtract a strip on one of the long sides
+A+=+%28+2x+%2B+15+%29%2A%28+2x+%2B+20+%29+-+15%2A20+-+20x+
+A+=+4x%5E2+%2B+30x+%2B+40x+%2B+300+-+300+-+20x+
+A+=+4x%5E2+%2B+50x+
--------------------------
+168+=+4x%5E2+%2B+50x+
+2x%5E2+%2B+25x+-+84+=+0+
Use quadratic formula
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+2+
+b+=+25+
+c+=+-84+
+x+=+%28-25+%2B-+sqrt%28+25%5E2+-+4%2A2%2A%28-84%29+%29%29%2F%282%2A2%29+
+x+=+%28-25+%2B-+sqrt%28+625+%2B+672+%29%29%2F+4+
+x+=+%28-25+%2B-+sqrt%28+1297+%29%29%2F+4+
+x+=+%28-25+%2B+36.014%29%2F+4+
+x+=+2.7535+ ft
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check:
+168+=+4x%5E2+%2B+50x+
+168+=+4%2A2.7535%5E2+%2B+50%2A2.7535+
+168+=+4%2A7.5816+%2B+137.675+
+168+=+30.3264+%2B+137.675+
+168+=+168.0014+
close enough
check the math & get 2nd opinion if needed