Answer:
Step-by-step explanation:
Sure! Let's start with ratios and proportions, which are both ways of comparing quantities with each other using numbers. A ratio is simply a comparison of two quantities using a colon or a fraction bar between them, like this: a : b or a / b . For example, if we have a recipe that calls for twice as much salt as pepper (let's say we need two teaspoons of salt for every teaspoon of pepper), we can represent this as a ratio: 2 : 1 or 2/1 .
A proportion, on the other hand, is a special kind of ratio where the product of the two quantities is the same as the product of their corresponding quantities in another ratio with the same relationship between the quantities. In other words, if we have two ratios, a : b and c : d, and we want to find out if they are proportional, we need to make sure that their products are equal: a * d = b * c .
Let's say we have a rectangle with a length of 15 units and a width of 6 units. We want to find the perimeter of this rectangle, which is the total distance around the outside of the rectangle. To do this, we need to add up the lengths of all four sides. Let's call the length of the rectangle "l", the width of the rectangle "w", and the perimeter of the rectangle "P".
First, let's find the length of the rectangle's two shorter sides (the sides next to the width):
Short side 1 = l - w
Short side 2 = l - w
Now, let's find the length of the rectangle's two longer sides (the sides next to the length):
Long side 1 = w
Long side 2 = w
Finally, let's add up all four sides to find the perimeter:
P = short side 1 + short side 2 + long side 1 + long side 2
Substituting our expressions for the lengths, we get:
P = l - w + l - w + w + w
Simplifying, we get:
P = 2l - 2w
Now, let's say we want to find the perimeter of a rectangle with a length of 20 units and a width of 8 units. We can use our formula to calculate the perimeter:
P = 2 * 20 - 2 * 8
P = 40 - 32
P = 8
So the perimeter of the rectangle with a length of 20 units and a width of 8 units is 8 units.
I hope that helps clarify ratios, proportions, and how to find the perimeter of a rectangle! Let me know if you have any other questions.
