Question

The triangle, $\Delta XYZ$, shown above has sides of lengths $x,y$ and $z$ inches and is not a right angled triangle. Let $X^{\prime }$ be the image of $X$ when the triangle is reflected across $\overline{YZ}$. Find the correct expression for the perimeter, in inches, of quadrilateral $X^{\prime },YXZ$.

• A. $2(y+z)+x$
• B. $2(x+y+z)$
• C. $2(x+y)$
• D. $2(x+z)$
• E. $2(y+z)$

Answer 1

Answer: (E)

$2(y+z)$

Reflecting the triangle over $YZ$ will create a parallelogram with the vertices $X$, $Y$, $X^{\prime }$ ($X$ prime), and $Z$.

The perimeter of a polygon is the sum total of the sides.

In this case, the sides will sum to: $z+y+z+y$.

Factoring this will give us: $2z+2y$.

Factoring again will leave $2(z+y)$ or $2(y+z)$.