Rectangle Perimeter with 4×8 Dimensions and Embedded Equilateral Triangle

Look at the following rectangle:

AAABBBCCCDDDEEE84

ΔEDC is equilateral.

Calculate the perimeter of the rectangle.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the perimeter of the rectangle
00:03 Equilateral triangle according to the given data
00:06 Opposite sides in a rectangle are equal
00:20 The perimeter of the rectangle equals the sum of its sides
00:32 Let's solve every 2 factors separately and then sum them
00:39 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the following rectangle:

AAABBBCCCDDDEEE84

ΔEDC is equilateral.

Calculate the perimeter of the rectangle.

2

Step-by-step solution

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=

24

3

Final Answer

24

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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