The length of a rectangle is 5/16 of its perimeter. Find the width of this rectangle if its length is 80 cm.

Find what the perimeter of the rectangle is
From the problem statement, we know that the length of the rectangle is 5/16 of its perimeter. And, in turn, the corresponding length of this rectangle is 80 cm.

To find the perimeter, it is convenient for us to draw up a proportion in which:

denote the required value as x;
we take this value as a whole, that is, we equate it to one;
equate 80 cm to 5/16 (according to the condition of the problem).
Therefore, we get a system that will look like this:

x = 1

80 = 5/16

Express x from the given proportion. To do this, we need to use the rule of proportion or the rule of the cross:

The product of the extreme terms of the proportion is correspondingly equal to the product of its middle terms.

Or in other words: if we draw a cross on our proportion, then the product of the members at the ends of this cross are respectively equal.

Therefore, we get the expression:

x * 5/16 = 1 * 80

Express x and get:

x = 1 * 80 / 5/16 = 80 / 5/16 = 80 * 16/5 = 16 * 16 = 256

Thus, we get that the perimeter of this rectangle is 256 cm.

Find the width of the given rectangle
We know that the perimeter of any figure is found as the sum of the lengths of all its sides. Since a rectangle has two opposite sides, respectively, equal, therefore, the formula for finding the perimeter of a rectangle is:

P = 2 * (a + b)

Where:

P is the perimeter of the rectangle;
a – its length;
b – the width of the rectangle, respectively.
From the condition:

P = 256 cm;

a = 80 cm.

Then:

2 * (80 + b) = 256;

80 + b = 128;

b = 128 – 80;

b = 48

That is, the width of the rectangle is 48 cm.

Answer: 48 cm