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

Question

Rectangle ABCD contains three other rectangles inside of it.

Calculate the perimeter of rectangle ABCD.

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

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

$EF=BH=AG=5$

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:

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