Rectangle Perimeter with 4×8 Dimensions and Embedded Equilateral Triangle

Question

Look at the following rectangle:

ΔEDC is equilateral.

Calculate the perimeter of the rectangle.

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

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=