Calculate Rectangle Perimeter: Triangle Perimeter = 20 with Side X+2

Question

Look at the following rectangle:

Given that the perimeter of the triangle BCD is 20, what is the perimeter of the rectangle ABCD?

00:00 Calculate the perimeter of the rectangle

00:06 The perimeter of the triangle equals the sum of its sides

00:17 Let's substitute appropriate values according to the given data and solve for X

00:34 Collect terms

00:41 Isolate X

00:45 This is the value of X, let's substitute to find the side length

00:56 Opposite sides are equal in a rectangle

01:11 The perimeter of the rectangle equals the sum of its sides

01:15 Let's substitute appropriate values and solve for the perimeter

01:35 And this is the solution to the question

Given that the perimeter of triangle BCD is 20

We can therefore insert the existing data and calculate as follows:

$20=10+6+x+2$

$20=16+x+2$

$20-16-2=x$

$x=2$

Now we can calculate the BC side: 2+2=4

Perimeter of the rectangle ABCD:

$6+6+4+4=12+8=20$