Original
Length (L): L
width (w): w
Perimeter (P) = 2L + 2w
48 = 2(L) + 2(w)
24 = L + w
24 - L = w
*******************************************
New
Length (L): L + 24
width (w): 2w ⇒2(24 - L) = 48 - 2L
Perimeter (P) = 2L + 2w
112 = 2(L + 24) + 2(48 - 2L)
112 = 2L + 48 + 96 - 4L
112 = -2L + 140
-28 = -2L
14 = L
Answer: 14 m
Answer:
The answer is 16
Step-by-step explanation:
Firstly, we have to determine two equations that represent the perimeter before and after of changings.
Let
W=width of the rectangle
L=length of the rectangle
P=perimeter of the rectangle
Before of changings:
[tex]P=2*W+2*L\\P=48\\48=2*W+2*L[/tex]
After of changings:
[tex]P=2*(2*W)+2*(L+24)\\\\P=4*W+2*L+48\\P=112\\112=4*W+2*L+48\\64=4*W+2*L[/tex]
Finally, we resolve both equations:
[tex](-1)*(48)=(-1)*(2*L+2*W)\\-48=-2*W-2*L\\\\64=4*W+2*L\\\\[/tex]
Adding both equations:
[tex]-48+64=-2*W-2*L+4*W+2*L\\16=2*W\\W=16/2=8\\\\[/tex]
Replacing W value in any equation:
[tex]64=4*8+2*L\\64=32+2*L\\2*L=64-32\\2*L=32\\L=32/2=16\\[/tex]
Then, the length of the original rectangle (before changings) is 16
