Calculate Rectangle ABCD Perimeter: Nested Rectangles with Measurements 3, 5, 6, and 7

Rectangle ABCD contains three other rectangles inside of it.

Calculate the perimeter of rectangle ABCD.

AAABBBCCCDDDGGGHHHEEEFFF6753

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the perimeter of rectangle ABCD
00:08 Opposite sides are equal in rectangle EBHF
00:50 The whole side equals the sum of its parts
00:57 Opposite sides are equal in rectangle ABCD
01:08 The whole side equals the sum of its parts
01:19 Opposite sides are equal in rectangle ABCD
01:22 The perimeter of the rectangle equals the sum of its sides
01:32 Let's substitute appropriate values and solve for the perimeter
01:55 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Rectangle ABCD contains three other rectangles inside of it.

Calculate the perimeter of rectangle ABCD.

AAABBBCCCDDDGGGHHHEEEFFF6753

2

Step-by-step solution

Since in a rectangle, each pair of opposite sides are equal to one another, we can deduce that:

EF=BH=AG=5 EF=BH=AG=5

We can calculate side AD:

5+3=8 5+3=8

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

FH=EB=6 FH=EB=6

Now we can calculate side AB:

7+6=13 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 8+13+8+13=16+26=42

3

Final Answer

42

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?
666444AAABBBCCCDDD

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