SOLUTION: a rectangular garden measure 6 m by 9 m and is surrounded by a walkway of uniform width. If the area of the walkways 23 m2 less than the garden find the width of the walkway

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: a rectangular garden measure 6 m by 9 m and is surrounded by a walkway of uniform width. If the area of the walkways 23 m2 less than the garden find the width of the walkway      Log On


   

Question 1083156: a rectangular garden measure 6 m by 9 m and is surrounded by a walkway of uniform width. If the area of the walkways 23 m2 less than the garden find the width of the walkway
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39613) About Me  (Show Source):
You can put this solution on YOUR website!
Garden Area, %286-2x%29%289-2x%29

Walkway area, 6%2A9-%286-2x%29%289-2x%29
6%2A9-6%2A9%2B18x%2B12x-4x%5E2
30x-4x%5E2

DESCRIPTION:
30x-4x%5E2=4x%5E2-30x%2B54-23
Simplify and solve this for x.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+6%2A9+=+54+ m2
and
+54+-+23+=+31+ m2
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The combined area of the garden and walkway is
+54+%2B+31+=+85+ m2
Let +x+ = the width of the walkway
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+%28+6+%2B+x+%29%2A%28+9+%2B+x+%29+=+85+
+54+%2B+15x+%2B+x%5E2+=+85+
+x%5E2+%2B+15x+-+31+=+0+
+x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+a+=+1+
+b+=+15+
+c+=+-31+
+x+=+%28-15+%2B-+sqrt%28+15%5E2-4%2A1%2A%28-31%29+%29%29%2F%282%2A1%29+
+x+=+%28-15+%2B-+sqrt%28+225+%2B+124+%29%29%2F2+
+x+=+%28-15+%2B-+sqrt%28+349+%29%29%2F2+
+x+=+%28+-15+%2B+18.68+%29+%2F+2+
+x+=+3.68%2F2+
+x+=+1.84+
The width of the walkway is 1.84 m
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check:
+%28+6+%2B+x+%29%2A%28+9+%2B+x+%29+=+85+
+%28+6+%2B+1.84+%29%2A%28+9+%2B+1.84+%29+=+85+
+7.84%2A10.84+=+85+
+84.986+
close enough -error due to rounding off, I think
check the math