Question

1. xz = n, wz = 2n - 5, and the perimeter of △xwz is 20. what is the value of n?

7
3
5
6

Explanation:

Step1: Recall perimeter formula

The perimeter of $\triangle XWZ$ is $P = XZ+WZ + XW$. Since $XW = WZ$ (from the markings on the triangle), $P=XZ + 2WZ$. Substitute $XZ=n$, $WZ = 2n - 5$ and $P = 20$ into the formula: $20=n + 2(2n-5)$.

Step2: Expand the equation

Expand $2(2n - 5)$ using the distributive property $a(b - c)=ab - ac$. So $2(2n-5)=4n-10$. The equation becomes $20=n + 4n-10$.

Step3: Combine like - terms

Combine the $n$ terms on the right - hand side: $n+4n=5n$. The equation is now $20 = 5n-10$.

Step4: Solve for $n$

Add 10 to both sides of the equation: $20 + 10=5n-10 + 10$, which simplifies to $30 = 5n$. Then divide both sides by 5: $\frac{30}{5}=\frac{5n}{5}$, so $n = 6$.

Answer:

6