Rectangle Perimeter with Congruent Triangles: Finding Total Length Using 10, 5, and 8

Look at the following rectangle:

ΔEAG≅ΔFCH

Find the perimeter of rectangle EFCD.

Since the triangles are equal to each other, we can claim that:

$AE=FC$

$AG=CH=8$

$EG=FH=10$

Now let's calculate side AB:

$8+5=13$

Since in a rectangle each pair of opposite sides are equal to each other:

$AB=CD=13$

We can also claim that:

$DH=13-8=5$

Side EF is also equal in length to sides AB and CD which are equal to 13

Now let's calculate side FC using the Pythagorean theorem in triangle FCH:

$HC^2+FC^2=HF^2$

Let's input the known data:

$8^2+FC^2=10^2$

$64+FC^2=100$

$FC^2=100-64$

$FC^2=36$

Let's take the square root:

$FC=6$

Now we can calculate the perimeter of rectangle EFCD by adding all sides together:

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