SOLUTION: A rectangular plot, 16 ft by 15 ft, is to be used for a garden. It is decided to put a pavement inside the entire border so that 132 square feet of the plot is left for flowers. Ho

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: A rectangular plot, 16 ft by 15 ft, is to be used for a garden. It is decided to put a pavement inside the entire border so that 132 square feet of the plot is left for flowers. Ho      Log On

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Question 945714: A rectangular plot, 16 ft by 15 ft, is to be used for a garden. It is decided to put a pavement inside the entire border so that 132 square feet of the plot is left for flowers. How wide should the pavement be?
If you could help me with this I would appreciate it

Found 2 solutions by MathLover1, josmiceli:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


L=16ft ,W=15ft
to make a pavement, xft is deducted from each side; so, 2x from the length and 2x from the width
A=%28L-2x%29%2A%28W-2x%29
132=%2816-2x%29%2A%2815-2x%29
132=240-31x-30x%2B4x%5E2
132=240-61x%2B4x%5E2
0=240-132-61x%2B4x%5E2
4x%5E2-61x%2B108=0
=>x=+2 or x+=+27%2F2=13.5 (this one is to high and we cannot use it)
we can use DISABLED_event_only= >highlight%28x=+2%29
and dimensions of the 132 square feet plot are:
L%5Bplot%5D=16ft-2%2A2ft+=12ft
W%5Bplot%5D=15ft-2%2A2ft=11ft
check the area:
12ft%2A11ft=132ft%5E2 as given

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
It sounds like the pavement is the
same width all the way around
Let +x+ = the width of the pavement
-----------------------
+16%2A15+=+240+ ft2 is the outside area
-----------------------
+%28+16+-+x+%29%2A%28+15+-+x+%29+=+132+
+240+-+15x+-+16x+%2B+x%5E2+=+132+
+x%5E2++-+31x+%2B+108+=+0+
Use the quadratic equation
+x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-31+
+c+=+108+
+x+=+%28+-%28-31%29+%2B-+sqrt%28+%28-31%29%5E2+-+4%2A1%2A108+%29%29+%2F+%282%2A1%29+
+x+=+%28+31+%2B-+sqrt%28+961+-+432+%29%29+%2F+2+
+x+=+%28+31+%2B-+sqrt%28+529+%29%29+%2F+2+
+x+=+%28+31+-+23+%29+%2F+2+
+x+=+8%2F2+
+x+=+4+ ( the positive square root makes no sense )
The width of the pavement is 4 ft
check:
+%28+16+-+x+%29%2A%28+15+-+x+%29+=+132+
+%28+16+-+4+%29%2A%28+15+-+4+%29+=+132+
+12%2A11+=+132+
+132+=+132+
OK