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Perimeter of rectangle by diagonal.
Common Core Standard: 6.G.1 6th Grade Math
Two additional “Perimeter of a Rectangle" Videos
Perimeter of a rectangle calculator
Perimeter of a square
Formula for finding the perimeter of a square:
Because a square has four equal sides you can use 4 x S
or
You can also treat a square like a rectangle and use the formula for a rectangle.
2 x length + 2 x width
S
S
S
S
S = side length of the square
Video # 1
Answers the following questions
How do you find the perimter of a rectangle that measures 5x8 units?
Video # 2
How do you find the perimeter of a rectangle using side length and diagonal length?
Example problem two involves finding the perimeter of a triangle in which you only have a measurement of one side and the diameter. You can use the property of a rectangle that states a rectangle has four right angles. As a result the diagonal creates a right triangle.
Problem one uses the formula 2 x length + 2 x width
Problem two uses the diagonal to find the missing side then the perimeter formula
Perimeter of a rectangle
Step 1. Find the length of the two missing sides, this is easy because opposite sides are congruent so the four sides are 8, 8, 12, 12 units.
Step 2. Add the side lengths together.
8+8+12+12=40 units
Step 3. Another method is to use the perimeter of a rectangle formula 2*length + 2* Width
2*8 + 2*12
16 + 24 = 40 units
Example problem 1. Find the perimeter of a rectangle with one side of 8 units and one side of 12 units.
Example problem 2. Find the perimeter of a rectangle with a diagonal of 13 units and a side length of 12 units.
Step 1. A rectangle has four right angles and the diagonal creates a right triangle. As a result, the diagonal can be labeled the hypotenuse of the right triangle.
Step 2. Use the Pythagorean Theorem to find the length of the missing side. Let’s label c=13 (the diagonal) a = 12 (the side length we are given) and solve for b
Step 3. Use the Pythagorean Theorem a^2+b^2=c^2
Step 3a. 12^2+b^2=13^2
Step 3b. 144+b^2=169
(Subtract 144 from each side)
Step 3c. b^2=25
Step 3d. b=√(25 ) b=5 units
Step 4. Now you can plug this side length into the formula for the perimeter of a rectangle
2*length + 2*width = perimeter
2*5 + 2*12 = 10 +24= 34 units
Perimeter rectangle problems
Related Sites covering Perimeter of a Rectangle
Perimeter Rectangle/Worksheets/Mathworksheets4kids A large variety of free worksheets covering perimeter
Word problems involving rectangle perimeter/algebra.com This link includes six word problems in which you have to calculate the perimeter of the rectangle in order to solve the problem. Each word problem includes step by step directions on how to solve the problem.
What is a rectangle? Basic properties and a labeled picture of a rectangle from Dr. Math