Let's assume the length of the rectangle be l and width is w.
Given that, the rectangle has a width of 50 centimeters .
So, w = 50.
And Perimeter = 204.
Since, the formula for perimeter of a rectangle is 2l + 2w. So, we can set up an equation as following:
2l +2w = 204
2l + 2(50) = 204 Since, w = 50 is given.
2l + 100 = 204
2l + 100 - 100 = 204 - 100 Subtract 100 from each sides.
2l = 104
[tex] \frac{2l}{2} =\frac{104}{2} [/tex] Divide each sides by 2 to isolate l.
So, l = 52
Therefore, length of rectangle is 52 centimeters.
The perimeter of a rectangle is [tex] p=2(l+w) [/tex], where [tex] l [/tex] is the length and [tex] w [/tex] width of the perimeter. Here [tex] p=204,w=50 [/tex].
Hence,
[tex] 2(50+l)=204\\
50+l=102\\
l=52 [/tex]
The rectangle's length is [tex] 52\;cm [/tex]
