Question

The perimeter of the given triangle is $11.1$ centimeters. Find the length of side $YZ.$

• A. $3.4cm$
• B. $5.4cm$
• C. $4.8cm$
• D. $6.8cm$

Answer 1

The correct option is A $3.4cm$

Using the interior angle sum property of a triangle,

$\angle X+\angle Y+\angle Z={180}^{\circ }$
$\Rightarrow \angle X+50+80={180}^{\circ }$
$\Rightarrow \angle X+130={180}^{\circ }$
$\Rightarrow \angle X=180-{130}^{\circ }$
$\Rightarrow \angle X={50}^{\circ }$

As $\angle X=\angle Y$
Hence, this is an isosceles triangle.
$\Rightarrow YZ=XZ$

Perimeter of a triangle = sum of all sides
$\Rightarrow XY+YZ+XZ=11.1cm$
$\Rightarrow 4.3+2YZ=11.1(YZ=XZ)$
$\Rightarrow 2YZ=11.1-4.3$
$\Rightarrow 2YZ=6.8$
$\Rightarrow YZ=\frac{6.8}{2}$
$\Rightarrow YZ=3.4cm$