SOLUTION: a landscape architect is designing a rectangular flowerbed to be border with 28 plants that are placed 1 meter apart. He needs an inner rectangular space in the center for plants t

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a landscape architect is designing a rectangular flowerbed to be border with 28 plants that are placed 1 meter apart. He needs an inner rectangular space in the center for plants t      Log On


   

Question 1061736: a landscape architect is designing a rectangular flowerbed to be border with 28 plants that are placed 1 meter apart. He needs an inner rectangular space in the center for plants that must be 1 meter from the border of the bed and that require 24 square meters for planting. What should the overall dimensions of the flowerbed be?
how should i tackle this kind of problem when solving?
thank you!!!
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I think if you were to walk around the flowerbed,
there would be +28+-+1+=+27+ m
This tells me that:
+2L+%2B+2W+=+27+
+2L+=+27+-+2W+
--------------------------------
From the other data I conclude that:
+%28+L+-2+%29%2A%28+W+-+2+%29+=+24+
+L+-+2+=+24%2A%28+1%2F%28+W+-+2+%29%29+
multiply both sides by +2+
+2L+-+4+=+48%2A%28+1%2F%28+W-2+%29%29+
+27+-+2W+-+4+=+48%2A%28+1%2F%28W-2%29%29+
+-2W+%2B+23+=+48%2A%28+1%2F%28W-2%29%29+
+%28+-2W+%2B+23+%29%2A%28+W+-+2+%29+=+48+
+-2W%5E2+%2B+23W+%2B+4W+-+46+=+48+
+-2W%5E2+%2B+27W+-+94+=+0+
Use quadratic formula
+W+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
+W+=+%28-27+%2B-+sqrt%28+27%5E2-4%2A%28-2%29%2A%28-94%29+%29%29%2F%282%2A%28-2%29%29+
+W+=+%28-27+%2B-+sqrt%28+27%5E2-4%2A%28-2%29%2A%28-94%29+%29%29%2F%28-4%29%29+
You can finish -find +W+ then +L+
Check all my math, too