Rectangle Perimeter Problem: Using Triangle Area of 9 to Find Solution

Question

Look at the following rectangle:

Given that the area of the triangle ABD is 9, what is the perimeter of the rectangle ABCD?

00:00 Calculate the perimeter of the rectangle

00:03 We'll use the formula for calculating triangle area

00:07 (height multiplied by side) divided by 2

00:27 Divide 6 by 2

00:34 Open parentheses properly, multiply by each factor

00:44 Isolate X

00:53 This is the value of X, let's substitute to find the side length

01:09 Opposite sides are equal in a rectangle

01:23 The perimeter of the rectangle equals the sum of its sides

01:30 Let's substitute appropriate values and solve for the perimeter

01:45 And this is the solution to the question

Area of triangle ADB:

$\frac{AD\times AB}{2}$

Let's list the known data:

$9=\frac{x+2\times6}{2}$

$9=(x+2)\times3$

$9=3x+6$

$9-6=3x$

$3=3x$

$1=x$

Side AD equals:

$1+2=3$

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

$AD=BC=3$

$AB=CD=6$

Now we can calculate the perimeter of the rectangle:

$3+6+3+6=6+12=18$