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?

S=8XS=8XS=8XX+4X+4X+4XXXAAABBBCCCDDD

Video Solution

Solution Steps

00:00 Calculate the area of the rectangle ABCD
00:03 Apply the formula for calculating the area of a triangle
00:08 (base(X+4) x height(X)) divided by 2
00:14 Substitute in the relevant values and proceed to 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 given that triangles ABC and ACD are congruent (S.S.S.)
01:01 Substitute in the relevant values and solve for the area
01:16 This is the solution

Step-by-Step Solution

Let's calculate the area of triangle ABC:

8x=(x+4)x2 8x=\frac{(x+4)x}{2}

Multiply by 2:

16x=(x+4)x 16x=(x+4)x

Divide by x:

16=x+4 16=x+4

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

164=x 16-4=x

12=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:

16×12=192 16\times12=192

Answer

192