Solve for X: Rectangle Perimeter 26 with Sides (X+2) and (X+3)

Question

Look at the following rectangle:

The perimeter of the rectangle is 26.

Calculate the value of X.

00:00 Find X

00:05 Opposite sides are equal in a rectangle

00:26 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

01:06 Collect like terms

01:22 Isolate X

01:36 And this is the solution to the question

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

$AD=BC=x+2$

$AB=CD=x+3$

Since the perimeter of the rectangle is equal to 26, we can substitute the data into the formula:

$26=x+2+x+3+x+2+x+3$

$26=4x+10$

$26-10=4x$

$16=4x$

Let's divide both sides by 4:

$4=x$