SOLUTION: I have a rectangle 100cm (L) x 50cm (W) = 5000cm (area) = L:W ratio 2:1 (2.0) I want to know if i have a rectangle with 50% of this area i.e. 2500cm How do i calculate the l

Algebra ->  Rectangles -> SOLUTION: I have a rectangle 100cm (L) x 50cm (W) = 5000cm (area) = L:W ratio 2:1 (2.0) I want to know if i have a rectangle with 50% of this area i.e. 2500cm How do i calculate the l      Log On


   

Question 917921: I have a rectangle 100cm (L) x 50cm (W) = 5000cm (area) = L:W ratio 2:1 (2.0)
I want to know if i have a rectangle with 50% of this area i.e. 2500cm
How do i calculate the length and width of this rectangle with the same ratio (2:1)?
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
L=100cm
W=50cm
A=5000cm%5E2
if A1=2500cm%5E2
=>L%5B1%5D%2AW%5B1%5D=2500cm%5E2
given:
L%3AW+=2%3A1 ......eq.1
L%5B1%5D%3AW%5B1%5D=2%3A1........eq.2
_______________________
so, L%3AW+=L1%3AW1
go to
L%5B1%5D%3AW%5B1%5D=2%3A1 .....eq.1..solve for L%5B1%5D
=> L%5B1%5D%2A1=W%5B1%5D%2A2
=> L%5B1%5D=2W%5B1%5D ..plug in L%5B1%5D%2AW%5B1%5D=2500cm%5E2

2W%5B1%5D%2AW%5B1%5D=2500cm%5E2+
2W%5B1%5D%5E2=2500cm%5E2
W%5B1%5D%5E2=2500cm%5E2%2F2+
W%5B1%5D%5E2=1250cm%5E2
W%5B1%5D=sqrt%281250cm%5E2%29
W%5B1%5D=35.35cm
then
L%5B1%5D=2W%5B1%5Dcm
L%5B1%5D=2%2A35.355cm
L%5B1%5D=70.71cm
check:
70.72cm%3A35.36cm=2%3A1 and
L%5B1%5D%2AW%5B1%5D=2500cm%5E2
=>70.72cm%2A35.36cm=2500cm%5E2
=>2499.95cm%5E2=2500cm%5E2 round it
=>2500cm%5E2=2500cm%5E2