Solve for X: Rectangle with Perimeter 20 and Sides 4X+3 and 2X+1

Question

Look at the following rectangle:

The perimeter of the rectangle is 20.

Calculate the value of X.

00:00 Find X

00:05 Opposite sides are equal in a rectangle

00:31 The perimeter of the rectangle equals the sum of its sides

00:39 Substitute appropriate values according to the given data and solve for X

01:11 Collect like terms

01:26 Isolate X

01:39 And this is the solution to the problem

Since in a rectangle every pair of opposite sides are equal, we can claim that:

$AD=BC=2x+1$

$AB=CD=4x+3$

Since the perimeter of the rectangle is equal to 20, we can substitute the data into the formula:

$20=2x+1+4x+3+2x+1+4x+3$

$20=12x+8$

$20-8=12x$

$12=12x$

Let's divide both sides by 12:

$1=x$

$1$