A rectangle has sides 9 cm and 8 cm. What is the perimeter
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Welcome to our lesson on calculating the perimeter of rectangles. The perimeter is the total distance around the outside of any shape. In real life, we use perimeter when fencing a garden, framing a picture, or measuring the boundary of a room. Understanding perimeter helps us solve practical problems involving boundaries and measurements.
A rectangle is a four-sided shape with four right angles, where opposite sides are equal in length. This means we have two pairs of equal sides. The longer sides are called the length, and the shorter sides are called the width. Every rectangle has these defining characteristics that make perimeter calculations straightforward.
In our problem, we have a rectangle with one side measuring 9 centimeters and another side measuring 8 centimeters. Since opposite sides of a rectangle are equal, we actually have two sides of 9 cm and two sides of 8 cm. Let's visualize this rectangle to better understand what we're working with.
Here we can see our rectangle clearly labeled with its dimensions. The top and bottom sides are both 9 centimeters long, while the left and right sides are both 8 centimeters long. This visual representation helps us understand that we need to add all four sides together to find the total perimeter.
To calculate the perimeter of any rectangle, we use the formula P equals 2 times the length plus 2 times the width. This formula accounts for both pairs of equal sides. We multiply each dimension by 2 because there are two sides of each length in every rectangle.
In our rectangle, we can designate the 9 centimeter sides as the length and the 8 centimeter sides as the width. It doesn't matter which we call length or width since the formula works the same way. The important thing is to identify both measurements correctly for our calculation.
Now we substitute our values into the formula: P equals 2 times 9 plus 2 times 8. This represents adding up all four sides of our rectangle. We're multiplying each dimension by 2 because we have two sides of each measurement.
Let's calculate step by step: first, 2 times 9 equals 18, and 2 times 8 equals 16. Now we add these results together: 18 plus 16 equals 34. This systematic approach ensures we don't miss any steps in our calculation.
We can also find the perimeter by adding all four sides individually: 9 plus 8 plus 9 plus 8. This gives us 17 plus 17, which also equals 34 centimeters. Both methods lead to the same answer, confirming our result is correct.
Since our original measurements were in centimeters, our perimeter must also be expressed in centimeters. The final answer is 34 centimeters. Always remember to include the appropriate units in your answer, as they tell us the scale and type of measurement we're dealing with.
Let's verify our answer makes sense: our rectangle has sides of 9 and 8 centimeters, so the perimeter should be greater than either dimension but reasonable for the given measurements. Thirty-four centimeters is logical for a rectangle of this size, confirming our calculation is correct.
If this rectangle represented a picture frame, you would need 34 centimeters of framing material. If it were a garden plot, you would need 34 centimeters of fencing to enclose it completely. This shows how perimeter calculations apply directly to real-world scenarios.