# Finding the perimeter of a rectangle.

How to find the perimeter of a rectangle.

The video link below works each problem. Hope it helps in class.

Let’s look at the step by step procedure  for finding the perimeter of a rectangle. First we need to look at some rectangle properties. A rectangle has opposite sides that are equal  and four right angles. Therefore if you know the length of one side then the opposite side will be the same length. The right angles allow the  diagonal to divide the rectangle into a right triangle.

Example problem 1. Find the perimeter of a rectangle with one side of 8 units and one side of 12 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 to find the perimeter of a rectangle is to use 2*length + 2* Width

2*8 + 2*12

16 + 24 = 40 units

Example problem 2. Find the perimeter if you have a rectangle with a diagonal of 13 units and a side length of 12 units. Step 1. Because a rectangle has four right angles the diagonal creates a right triangle with the diagonal being 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 a.12^2+b^2=13^2

Step b.144+b^2=169 (Subtract 144 from each side.

Step c. b^2=25

Step d.  b=√(25 ) b=5 units

Step 4. Now we know the missing side so I can use the formula for the perimeter of a rectangle

2*length + 2*width = perimeter

2*5 + 2*12 = 10 +24= 34 units