Perimeter of a Rectangle: Using Pythagoras' theorem

Look at the following rectangle:

Calculate the perimeter of the rectangle ABCD.

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:

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

28

The parallelogram ABCD contains the rectangle AEFC inside it, which has a perimeter of 24.

AE = 8

BC = 5

What is the area of the parallelogram?

In the first step, we must find the length of EC, which we will identify with an X.

We know that the perimeter of a rectangle is the sum of all its sides (AE+EC+CF+FA),

Since in a rectangle the opposite sides are equal, the formula can also be written like this: 2AE=2EC.

We replace the known data:

$2\times8+2X=24$

$16+2X=24$

We isolate X:

$2X=8$

and divide by 2:

$X=4$

Now we can use the Pythagorean theorem to find EB.

(Pythagoras: $A^2+B^2=C^2$)

$EB^2+4^2=5^2$

$EB^2+16=25$

We isolate the variable

$EB^2=9$

We take the square root of the equation.

$EB=3$

The area of a parallelogram is the height multiplied by the side to which the height descends, that is$AB\times EC$.

$AB=\text{ AE}+EB$

$AB=8+3=11$

And therefore we will apply the area formula:

$11\times4=44$

44

Look at the following rectangle:

ΔAEB is isosceles (AE=EB).

Calculate the perimeter of the rectangle ABCD.

$8+16\sqrt3$

Calculate the perimeter of following rectangle:

14

Look at the rectangle below.

EF divides DC into two equal parts.

Calculate the perimeter of the rectangle ABCD.

58

Look at the rectangle below:

Calculate the perimeter of rectangle ABCD.

28

Calculate the perimeter of the rectangle shown below:

28

Look at the rectangle below.

EF divides AD into two equal parts.

Calculate the perimeter of the rectangle ABCD.

62

Look at the following rectangle:

CE = AB

Calculate the perimeter of rectangle ABCD.

52

The rectangle ABCD is shown below.

ΔDBE is isosceles.

Calculate the perimeter of rectangle ABCD.

28

Look at the following rectangle:

ΔDEO ≅ ΔBFO

Calculate the perimeter of the rectangle ABCD.

28

The rectangle ABCD is shown below.

ΔDBE is isosceles.

Calculate the perimeter of rectangle ABCD.

14

The rectangle ABCD is shown below.

ΔDBE is isosceles.

Find the perimeter of rectangle ABCD.

34

The rectangle below is composed of two smaller rectangles.

EF is a segment that divides AD and BC into two equal parts.

Calculate the perimeter of the rectangle ABFE.

28

Look at the following rectangle.

What is its perimeter?

32

Look at the following rectangle:

The the area of the triangle ΔBCE is$\frac{1}{3}$ the area of the rectangle ABCD.

Calculate the perimeter of the rectangle ABCD.

60

The rectangle below is composed of two smaller rectangles.

EF divides AD and BC into two equal parts.

What is the perimeter of the rectangle ABCD?

36

Look at the following rectangle:

$ΔADE∼Δ\text{FCE}$

Calculate the perimeter of the rectangle ABCD.

72

Look at the following rectangle:

ΔEAG≅ΔFCH

Find the perimeter of rectangle EFCD.

$23+\sqrt{173}$