Question

select the correct answer. the area of the rectangle is 8 times the area of the triangle. find the value of x. x = select... 8 6 4 2

Explanation:

Step1: Calculate the area of the rectangle

The area formula for a rectangle is \(A = length\times width\). Here, the length is \(10\) and the width is \(x + 2\), so the area of the rectangle \(A_{rectangle}=10(x + 2)=10x+20\).

Step2: Calculate the area of the triangle

The area formula for a triangle is \(A=\frac{1}{2}\times base\times height\). Here, the base is \(x + 4\) and the height is \(2\), so the area of the triangle \(A_{triangle}=\frac{1}{2}\times2\times(x + 4)=x + 4\).

Step3: Set up the equation based on the given relationship

Since the area of the rectangle is \(8\) times the area of the triangle, we have the equation \(10x+20 = 8(x + 4)\).
Expand the right - hand side: \(10x+20=8x + 32\).
Subtract \(8x\) from both sides: \(10x-8x+20=8x - 8x+32\), which gives \(2x+20 = 32\).
Subtract \(20\) from both sides: \(2x+20-20=32 - 20\), so \(2x=12\).
Divide both sides by \(2\): \(x=\frac{12}{2}=6\).

Answer:

\(6\)