Perimeter of a Rectangle: Comprehension exercises

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:

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

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

$AB=CD=10$

$BC=AD=7$

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

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

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

$EF=BC=AD=5$

$FC=EB=3$

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

$AB=AE+EB$

Since 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:

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

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

$BC=AD=5$

Now we can calculate side ED:

$AD-AE=ED$

Let's substitute the known data:

$5-3=ED$

$ED=2$

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

We can also claim 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.

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

$EF=BH=AG=5$

Now we can calculate side AD:

$5+3=8$

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

$FH=EB=6$

Now we can calculate side AB:

$7+6=13$

Since side AB is equal to side CD, it is also equal to 13

Let's calculate the perimeter of rectangle ABCD:

$8+13+8+13=16+26=42$

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

$GH=AE=DF=9$

Now we can calculate side CD:

$9+5=14$

Since side CD is equal to side AB, it is also equal to 14

$BC=AD=7$

Let's calculate the perimeter of rectangle ABCD:

$7+14+7+14=14+28=42$

According to the data let's consider:

$CF=DE=3$

$AE=BF=5$

Now we can calculate BC:

$5+3=8$

$AD=BC=8$

Next we pay attention to any additional information and it seems that:

$GB=HC=4$

$DH=AG=7$

Hence we can calculate AB:

$7+4=11$

$AB=DC=11$

Lastly we can calculate the perimeter of the rectangle ABCD:

$8+8+11+11=$

$16+22=38$

According to the given data:

$JC=HB=3$

$DI=AG=3$

$FD=EC=3$

$BE=AF=4$

$GH=JI=6$

Now we can calculate sides AB and DC

$3+6+3=9+3=12$

And also sides AD and BC

$4+3=7$

Now we can calculate the perimeter of rectangle ABCD:

$12+7+12+7=24+14=38$

Based on the given data, we can claim that:

$HC=GB=8$

$ED=FC=4$

$AE=BC=10$

Now we can calculate side AE:

$AE=10-4=6$

$AE=BF=6$

Now we can calculate side AB which is equal to side CD:

$AB=CD=EF=8+5=13$

Now we can calculate the perimeter of rectangle ABFE:

$13+6+13+6=26+12=38$

A rectangle has two pairs of equal opposite sides.

That is:

BC=AD=4

AB=DC

In an equilateral triangle, all sides are equal, therefore:
EC=CD=DE

We know that EC=8, so:

EC=CD=DE=8

We know that:

AB=DC

Therefore:

AB=DC=8

Remember that the perimeter of a rectangle is equal to the sum of all its sides, therefore:

AB+BC+DC+AD

We substitute in all its known sides:

8+4+8+4=

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