In this lesson, students will learn how to find the unknown length of a side in a plane figure when the perimeter of the figure is known. |
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In the previous lesson, we learned how to find the perimeter of a shape by adding the length of each of the shape’s sides together. In this lesson, we will learn how to find missing lengths of the shape’s sides when the perimeter is known.
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In the grid, we have a rectangle with a perimeter of 20. Two of the sides are 6 inches long, one of the sides is 4 inches long, and the last side has an unknown length n. To solve for the value of n, let’s set up the equation for the perimeter of this rectangle 20 = 6 + 6 + 4 + n We can simplify the equation by adding 6,6, and 4 on the right side to get 20 = 16 + n Next, we can subtract 16 from both sides to get 4 = n So, we know the missing side length is equal to 4 inches. |
In the grid, we see a 6 sided shape with a perimeter of 24 centimeters. Two sides are 2 centimeters long, two other sides are 5 centimeters long, one side is 3 centimeters long, and the last side has an unknown length t. To solve for the value of t, let’s set up the equation for the perimeter of this rectangle 24 = 2 + 2 + 5 + 5 + 3 + t We can simplify the equation by adding 2, 2, 5, 5, and 3 on the right side to get 24 = 17 + t Next, we can subtract 17 from both sides to get 7 = t So, we know the missing side length is equal to 7 centimeters. |
In the grid, we see a square with a perimeter of 40 feet. None of the side lengths are known, however, we do know that a square has 4 equal sides. So we can set up the equation for perimeter as follows: 40 = r + r + r + r To solve for r, we simply need to find a number that is equal to 40 when added 4 times. Now, let us combined like terms on the right hand side of the equation to get 40 = 4 x r Next, we divide both sides of the equation by 4 to get r = 10 Which means that all sides of the square are 10 feet long. |
In the grid, we see the robot trace out a rectangle with a perimeter of 18 inches. We see that two of the sides of the rectangle are 6 inches long, but the other two sides are unknown. To solve for these unknown side lengths, recall that rectangles have two sides that are one length and two sides that are a different length. So, we know that the two missing side lengths must be equal. This means we can set up the equation for perimeter as follows: 18 = 6 + 6 + h + h We can simplify the right side of the equation by adding together 6 and 6 and also adding h and h to get 18 = 12 + (h + h) = 12 + (2 x h) Next, we can subtract 12 from both sides to get 6 = 2 x h To solve for h, we simply need to divide each side of the equation by 2. So, we know h = 3 Which means that the two missing sides are 3 inches long. |
