Find Rectangle Area: Using Triangle Area 8X and Side Length X+4

Question

Given the rectangle ABCD

Given BC=X and the side AB is larger by 4 cm than the side BC.

The area of the triangle ABC is 8X cm².

What is the area of the rectangle?

00:00 Calculate the area of rectangle ABCD

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

00:08 (base(X+4) times height(X)) divided by 2

00:14 We'll substitute appropriate values and solve for X

00:20 Multiply by 2 to eliminate the fraction

00:27 Reduce X from both sides of the equation

00:37 This is the length of side BC

00:47 The area of rectangle ABCD equals twice the area of triangle ABC

00:57 This is true because triangles ABC and ACD are congruent (S.S.S.)

01:01 We'll substitute appropriate values and solve for the area

01:16 And this is the solution to the problem

Let's calculate the area of triangle ABC:

$8x=\frac{(x+4)x}{2}$

Multiply by 2:

$16x=(x+4)x$

Divide by x:

$16=x+4$

Let's move 4 to the left side and change the sign accordingly:

$16-4=x$

$12=x$

Now let's calculate the area of the rectangle, multiply the length and width where BC equals 12 and AB equals 16:

$16\times12=192$

192