moomoomath logo header
lime green horizontal line
Welcome to MooMooMath
study skills A teachers secret guide to your best grades
Master the 7 pillars of school success

Improve your grades and lower your stress
A-Z Video List

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      

You can also treat a square like a rectangle and use the formula for a rectangle.
2 x length + 2 x width
perimeter of a square
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?
perimeter of a rectangle calculator
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.
white rectangle
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

perimeter rectangle 8 x12
rectangle diagonal 13 units

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/ 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