A rectangle is 15 cm by 9 cm. What is the perimeter
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A rectangle is a four-sided shape with four right angles. Opposite sides are equal and parallel. We typically label the longer side as length (l) and the shorter side as width (w).
The perimeter of a shape is the total distance around its outside. For a rectangle, we add up all four sides. Since opposite sides are equal, the perimeter equals twice the length plus twice the width, or equivalently, two times the sum of length and width.
Now let's solve a specific problem. We need to find the perimeter of a rectangle that is 15 centimeters by 9 centimeters. This means the length is 15 cm and the width is 9 cm. Our goal is to calculate the total distance around this rectangle.
Let's apply the perimeter formula P equals two times the sum of length and width. Substituting our values, we get P equals two times open parenthesis fifteen plus nine close parenthesis. First, we add fifteen plus nine to get twenty-four. Then we multiply two times twenty-four to get forty-eight. Therefore, the perimeter is forty-eight centimeters.
Let's verify our answer using the alternative perimeter formula: P equals two times length plus two times width. Substituting our values, we get P equals two times fifteen plus two times nine. This gives us thirty plus eighteen, which equals forty-eight centimeters. This confirms our previous result. We can also visualize this by adding each side: fifteen plus nine plus fifteen plus nine, which also equals forty-eight centimeters.
Let's practice with more examples. Example one: Find the perimeter of a rectangle with length twelve centimeters and width eight centimeters. Using our formula, P equals two times open parenthesis twelve plus eight close parenthesis, which equals two times twenty, giving us forty centimeters. Example two: Find the perimeter of a rectangle with length twenty centimeters and width six centimeters. We would set up the equation as P equals two times open parenthesis twenty plus six close parenthesis.