Question

a triangle has a height of (2n - 4) inches and a base of 8 inches. a rectangle has a length of 6 inches and a width of (3 + n) inches. the area in square inches of the triangle is equal to the area in square inches of the rectangle. what is the value of n? enter your answer in the box provided. n =

Explanation:

Step1: Calculate triangle area formula

The area formula for a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Given base $b = 8$ inches and height $h=(2n - 4)$ inches, so $A_{triangle}=\frac{1}{2}\times8\times(2n - 4)=4\times(2n - 4)=8n-16$.

Step2: Calculate rectangle area formula

The area formula for a rectangle is $A_{rectangle}=length\times width$. Given length $l = 6$ inches and width $w=(3 + n)$ inches, so $A_{rectangle}=6\times(3 + n)=18 + 6n$.

Step3: Set up the equation

Since the area of the triangle is equal to the area of the rectangle, we set up the equation $8n-16=18 + 6n$.

Step4: Solve the equation for $n$

Subtract $6n$ from both sides: $8n-6n-16=18 + 6n-6n$, which simplifies to $2n-16=18$. Then add 16 to both sides: $2n-16 + 16=18+16$, getting $2n=34$. Divide both sides by 2: $\frac{2n}{2}=\frac{34}{2}$, so $n = 5$.

Answer:

$n = 5$