Perimeter of a Rectangle - Examples, Exercises and Solutions

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

$AB=CD=2$

$AD=BC=7$

Now we can add all the sides together and find the perimeter:

$2+7+2+7=4+14=18$

In the drawing, we have a rectangle, although it is not placed in its standard form and is slightly rotated,
but this does not affect that it is a rectangle, and it still has all the properties of a rectangle.
 
The perimeter of a rectangle is the sum of all its sides, that is, to find the perimeter of the rectangle we will have to add the lengths of all the sides.
We also know that in a rectangle the opposite sides are equal.
Therefore, we can use the existing sides to complete the missing lengths.
 
4.8+4.8+12+12 =
33.6 cm

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

$AD=BC=9.5$

$AB=CD=1.5$

Now we can add all the sides together and find the perimeter:

$1.5+9.5+1.5+9.5=19+3=22$

Since in a rectangle all pairs of opposite sides are equal:

$AD=BC=5$

$AB=CD=9$

Now we calculate the perimeter of the rectangle by adding the sides:

$5+5+9+9=10+18=28$

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

$AB=CD=10$

$BC=AD=7$

Now let's add all the sides together to find the perimeter of the rectangle:

$10+7+10+7=20+14=34$

In a square, all sides are equal. Therefore:
$AB+BC+CD+DE+EF+FA=6$

Thus, we find out what the side AC is equal to:

$AC=AB+BC$

$AB=6+6=12$

In a rectangle, we know that the opposite sides are equal to each other, therefore:

$AB=FD=12$

Therefore, the formula for the perimeter of the rectangle will look like this:

$2\times AB+2\times CD$

We replace the data:

$2\times12+2\times6=$

$24+12=36$

Since every pair of opposite sides are equal to each other in a rhombus, we know that:

$EF=BC=AD=5$

$FC=EB=3$

To calculate side AB, we must use the following formula:

$AB=AE+EB$

As we are only given the length of EB, we don't have enough information and cannot calculate the lengths of the other sides.

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

$EF=BC=AD=5$

$FC=EB=3$

Now we can calculate side AB:

$8+3=11$

Since AB and CD are equal to each other, side CD is also equal to 11

Let's calculate the perimeter of the rectangle:

$11+5+11+5=22+10=32$

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

$AE=BF=5$

$AB=CD=9$

Now we can calculate side BC:

$5+3=8$

Since side BC is equal to side AD, it is also equal to 8

Let's calculate the perimeter of rectangle ABCD:

$9+8+9+8=18+16=34$

Since in a square all sides are equal to each other, all sides are equal to 8 cm.

Now we can calculate the perimeter:

$8\times4=32$

Given that in the smaller rectangle ED=CF=4 (each pair of opposite sides in the rectangle are equal)

We can therefore calculate for the rectangle ABCD that BC=6+4=10

Now we can state in the rectangle ABCD that BC=AD=10

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

DC=AB=15

Hence the perimeter of the rectangle ABCD is equal to:

$10+10+15+15=20+30=50$

In the statement, we have two rectangles that are connected by a common side,

The left quadrilateral, AEFD, has a known side - AD

The right quadrilateral, EBCF, also has only one known side: FC

In the question, we are asked for the perimeter of the rectangle ABCD,

For this, we need its sides, and since the opposite sides in a rectangle are equal, we need at least two adjacent sides.

We are given the side AD, but the side DC is only partially given.

We have no way of finding the missing part: DF, so we have no way of answering the question.

This is the solution!

Based on the given data, we know that:

$AD=BC=5$

$AB=AE+EB$

$AB=7+EB$

We are missing data to determine the length of AB, and therefore we cannot calculate the perimeter of the rectangle

Since every pair of opposite sides are equal in a rectangle, we know that:

$BC=AD=5$

Now we can calculate side ED:

$AD-AE=ED$

Let's substitute in the known data:

$5-3=ED$

$ED=2$

Side ED is equal to side FC and therefore also equal to 2.

We also know that:

$AB=CD=EF=7$

Now we can calculate the perimeter of rectangle EFCD:

$2+7+2+7=4+14=18$

Let's look at rectangle EBHF where we are given:

EF=BH=5

FH=EB=6

From this we can calculate AB:

7+6=13

Now we have a pair of sides in rectangle ABCD:

AB=DC=13

We know that EF=BH=AG=5

We therefore do not have enough additional data to calculate the sides AD and BC.