Calculate Rectangle Perimeter: 10 x 6 ABCD Rectangle

Question

Look at the following rectangle:

Calculate the perimeter of the rectangle ABCD.

00:00 Calculate the perimeter of the rectangle

00:03 Let's use the Pythagorean theorem in triangle BCD

00:15 Substitute appropriate values according to the given data and solve for DC

00:33 Isolate DC

00:48 This is the length of side DC

00:57 Opposite sides are equal in a rectangle

01:12 The perimeter of the rectangle equals the sum of its sides

01:20 Substitute appropriate values and solve for the perimeter

01:45 And this is the solution to the problem

Let's focus on triangle BCD in order to find side DC

We'll use the Pythagorean theorem and input the known data:

$BC^2+DC^2=BD^2$

$6^2+DC^2=10^2$

$DC^2=100-36=64$

Let's take the square root:

$DC=8$

Since in a rectangle each pair of opposite sides are equal to each other, we can state that:

$DC=AB=8$

$BC=AD=6$

Now we can calculate the perimeter of the rectangle by adding all sides together:

$8+6+8+6=16+12=28$