PART 1

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In this lesson, we will learn about the perimeter of a rectangle.

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Consider this rectangle. This rectangle has the length of L and the width of W.

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Since, the perimeter of the rectangle, P, is the total distance around the outside of the rectangle, the perimeter, will be equals to L, add with W, add with another L, and finally, add with another W.

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Let's simplify this. L add with L, gives 2L. Similarly, W add with W, gives 2W.

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Notice that, these two terms have '2' as a common factor.

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Hence, by taking out '2', we have, 2(L+W).

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Therefore, the perimeter, P = 2(L+W).

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Let's rewrite it here.

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Note that, in any calculation, when we found the value of P, it is important to include the unit.

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For example, if L and W are given in centimeter, the unit for the perimeter will be in centimeter as well.

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The next video will show some examples on using this formula.

PART2

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After understanding the formula for the perimeter of a rectangle, let's see some examples on using the formula.

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Find the perimeter of this rectangle, when its length is 4cm, and its width is 3cm.

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We start with the formula for the perimeter of a rectangle, P=2(L+W).

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Since the length of the rectangle is given as 4cm, we can substitute, L with 4.

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Similarly, since the width is given as 3cm, we can substitute W with 3.

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Let's simplify this. 4 add with 3, gives 7. 2 multiply with 7, gives 14.

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Hence, we have P=14.

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Now, this number doesn't mean anything, unless we include the unit for it.

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Since the length, and the width, are given in centimeter, the unit for the perimeter will also be in centimeter.

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Therefore, the perimeter of this rectangle is equals to 14cm.

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Next example, the perimeter of this rectangle, is 24ft, and its width is 5ft. Find its length.

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Again, we start with the formula for the perimeter of a rectangle, P=2(L+W).

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Since the perimeter, and the width of the rectangle are given, we can find the length of the rectangle, by solving this equation for L.

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Let's start. The perimeter is given as 24ft. Therefore, we can substitute P with 24.

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Similarly, since the width is given as 5ft, we can substitute W with 5.

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Now, to get a step closer in finding L, we need to remove '2'.

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To do so, we divide both sides of the equation with 2. This gives, 24 over 2, equals to L plus 5.

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24 divided by 2, gives 12.

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Now, we have, L plus 5, equals to 12.

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Let's rewrite this equation so that it looks neater.

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Next, to find L, we need to remove 5. To do so, we add -5 to both sides of the equation.

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By doing so, we get, L equals to 12 minus 5. 12 minus by 5, gives 7.

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Now, we have, L equals to 7. Note that, this number doesn't mean anything, unless we include the unit for it.

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Since the width is in feet, the length will also be in feet.

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Finally, the length of this rectangle is 7ft.

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That is all for this lesson. Try out the practice question to further your understanding.