SOLUTION: What is the dimensions of a rectangle with a area of 2888 square meter and 228 meters for perimeter? Thanks Joshua

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Question 1048563: What is the dimensions of a rectangle with a area of 2888 square meter and 228 meters for perimeter?
Thanks
Joshua
Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = length in meters
Let +b+ = width in meters
----------------------------
(1) +a%2Ab+=+2888+
(2) +2a+%2B+2b+=+228+
-----------------------
(1) +b+=+2888%2Fa+
By substitution:
(2) +2a+%2B+2%2A%28+2888%2Fa+%29+=+228+
(2) +2a+%2B+5776%2Fa+=+228+
(2) +2a%5E2+%2B+5776+=+228a+
(2) +2a%5E2+-+228a+%2B+5776+=+0+
(2) +a%5E2+-+114a+%2B+2888+
use qudratic formula
x+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+1+
+b+=+-114+
+c+=+2888+
+x+=+%28+-%28-114%29+%2B-+sqrt%28+%28-114%29%5E2+-+4%2A1%2A2888+%29%29+%2F+%282%2A1%29+
+x+=+%28+114+%2B-+sqrt%28+12996+-+11552+%29%29+%2F+2+
+x+=+%28+114+%2B+sqrt%28+1444+%29+%29+%2F+2+
+x+=+%28+114+%2B+38+%29+%2F+2+
+x+=+152%2F2+
+x+=+76+
( now make +x+=+a+, length in meters )
( not to be confused with the +a+ in
the quadratic formula )
+a+=+76+
and
(1) +a%2Ab+=+2888+
(1) +b+=+2888%2F76+
(1) +b+=+38+
The dimensions are 76 x 38
---------------------------
check:
(2) +2a+%2B+2b+=+228+
(2) +2%2A76+%2B+2%2A38+=+228+
(2) +152+%2B+76+=+228+
(2) +228+=+228+
OK

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let the length be L and the width W
the area of rectangle is A=L%2AW
the perimeter of rectangle is P=2L%2B2W

if we have a rectangle with a area of A=2888m%5E2 and P=228m for perimeter, than we have
L%2AW=2888m%5E2......eq.1
2L%2B2W=228m......eq.2
------------------------------solve this system
start with L%2AW=2888m%5E2, solve for L
L=2888m%5E2%2FW.......substitute in eq.2

2L%2B2W=228m......eq.2..first simplify this one
L%2BW=114......substitute L
2888%2FW%2BW=114.......both sides multiply by W
2888%2BW%5E2=114W
W%5E2-114W%2B2888=0........factor
W%5E2-38W-76W%2B2888=0
%28W%5E2-38W%29-%2876W-2888%29=0
W%28W-38%29-76%28W-38%29=0
%28W-76%29+%28W-38%29+=+0
solutions:
W=76m or W=38m
now find L
L=2888m%5E2%2F76m->L=38m
L=2888m%5E2%2F38m->L=76m
so,
L=76m and W=38m or the other way around