SOLUTION: The perimeter of a rectangle is 30cm; the area of the rectangle is 50cm square. Find the length and width of the rectangle. Please help! Thanks in advance!

Question 304957: The perimeter of a rectangle is 30cm; the area of the rectangle is 50cm square. Find the length and width of the rectangle.
Please help!
Thanks in advance!
Found 2 solutions by mananth, scutechandni10:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
2L+2W= perimeter = 30
L*w =Area = 50
L*W=50 l= 50/w
2L + 2W = 30
2*50/w +2W= 30
100/W + 2W=30
100+2W^2 / w = 30
100+2W^2= 30 W
2W^2-30W+100=0
W^2-15W+50=0
W^2-10W-5W+50=0
W(W-10)-5(w-10)=0
(W-5)(W-10)=0
W= 5 Or 10
The sides of the rectangle are 5 by 10

Answer by scutechandni10(7) (Show Source): You can put this solution on YOUR website!
Perimeter is 30cm
Area= 50cm2
Now,form simultaneous equation;
2l+2w=30
l*w=50
l=50/w
substitute into first equation:
2(50/w)+2w=30
100/w+2w=30
find LCM of w and 1; that is w
Therefore; (100 + 2w square)/w = 30
Multiply by w both sides to cancel(to get rid of) the denominator
w * 100+ 2w square/w = 30 * w
Therefore; 100+2w square = 30w
2w^2 - 30w + 100 = 0
Now this becomes a quadratic equation;
a= 2 b=-30 c= 100
now you substitute the values of a b and c in the formula.
ORR
By factorization;
Splitting the middle term;
2w^2-30w+100=0
2w^2-20w-10w+100=0
(2w^2-20w)+ (-10w+100)=0
2w(w-10)- 10(w-10)=0
Either (2w+10) (w-10) = 0
2w+10=0 w-10=0
2w=-10 w=+10
w= -5
Note: Length or width cannot be in negative therefore length is 10cm and width is 5cm
Note: ^2 means "square"

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