Let W be the width and let L be the length. We can set up the following two equations:
.45W = L
2W + 2L = 58
Now substitute the value for L in the first equation into the second.
2W + 2(.45W) = 58
2W + .9W = 58
2.9W = 58
W = 20
To find the length, we can plug this value for W back in to the first equation and find that
.45*20 = L
L = 9
So, the width of the rectangle is 20 cm and the length is 9 cm.
The width of a rectangle is 45% of the length.
Let the length of the rectangle be L, the width of the rectangle is 0.45*L
The perimeter of a rectangle with sides W and L is 2*(W + L)
Here, the perimeter is 2*(L + 0.45*L) = 58
2*1.45L = 58
2.9*L = 58
L = 20
The width of the rectangle is 0.45*20 = 9 cm.
We'll consider x as the length of the rectangle.
We'll note the width of the rectangle as w. We know, from enunciation that the width is:
w = 45*x/100
Now, we'll write the formula of the perimeter of the rectangle:
P = x + x + w + w
P = 2x + 2w
We'll substitute w by the ratio 45*x/100:
P = 2(x + 45*x/100)
We also know, from enunciation, that the perimeter of the rectangle is of 58 cm.
58 = 2(x + 45*x/100)
We'll divide by 2:
29 = x + 0.45x
29 = 1.45x
We'll divide by 1.45:
x = 29/1.45
x = 20 cm
The length of the rectangle is of 20 cm and the width is:
w = 0.45*20 cm
w = 9 cm