SOLUTION: The perimeter of a rectangle is 22cm and its area is 24 square cm. What are the lengths of its sides?

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Question 103664: The perimeter of a rectangle is 22cm and its area is 24 square cm.
What are the lengths of its sides?
Found 2 solutions by MathLover1, Fombitz:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
let
perimeter+=+P
area+=+A
sides: a%2C+and+b
P+=+2%28a%2Bb%29
since P+=+22cm
22+cm+=+2%28a+%2B+b%29 divide both sides by 2
11cm+=+a+%2B+b = > a+=+11+-+b
now
A+=+a%2Ab
since A+=+24+cm%5E2 and a+=+11+-+b
we have:
24+cm%5E2+=+%2811+-+b%29%2Ab+
24+cm%5E2+=+11b+-+b%5E2
b%5E2+-+11b+%2B+24+cm%5E2
b%281%2C2%29=%2811+%2B-+sqrt+%28%28-11%29%5E2+-4%2A1%2A24%29%29+%2F+%282%2A1%29
b%281%2C2%29=%2811+%2B-+sqrt+%28121+-96%29%29+%2F+%282%29
b%281%2C2%29=%2811+%2B-+sqrt+%2825%29%29+%2F+2
b%281%2C2%29=%2811+%2B-+5%29+%2F+2
b%281%29=%2811+%2B+5+%29%2F+2 = > b1+=+8

b%282%29=%2811+-5%29+%2F+2 = > b2+=+3+

since a+=+11+-+b
we have:
a+=+11+-+b1 => a1+=+11+-+8 or a1+=+3
a+=+11+-+b2 => a1+=+11+-+3 or a1+=+8
=>
a+=+8cm
b=+3+cm or vice versa
check:
P=+2%28a%2Bb%29
P+=+2%288%2B3%29
P+=+2%2A11
P+=+22cm
A=+8%2A3cm%5E2
A+=+24cm%5E2

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
L-length of the rectangle
W-width of the rectangle
P-perimeter of the rectangle
A-area of the rectangle
P=2L%2B2W=22 Perimeter equation.
A=L%2AW=24 Area equation.
L%2AW=24
L=24%2FWFind L as a function of W.
2L%2B2W=22
2%2824%2FW%29%2B2W=22Plug the value in the perimeter equation.
48%2FW%2B2W=22
48%2B2W%5E2=22W
2W%5E2-22W%2B48=0
W%5E2-11W%2B24=0Quadratic equation.
%28W-3%29%28W-8%29=0Factor the equation.
W=3 and W=8
When W=3, then
L=24/W=24/3=8
When W=8, then
L=24/W=24/8=3
Your two solutions are
W=3 cm, L=8 cm and W=8 cm, L=3 cm