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In the figure shown MN is parallel to segment YZ what is the length of segment YZ

User Mayuran
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1 Answer

4 votes

We will solve this question using the similar angle theorem

The shape consist of two triangles which i am going to draw out,

One is a big triangle while the other is a small triangle

Let NZ = a

To find NZ We will equate the ratio of the big triangle to that of the small triangle


\frac{7.5\operatorname{cm}}{3\operatorname{cm}}=\frac{(a+5)cm}{5\operatorname{cm}}

We then cross multiply to get,


\begin{gathered} 3(a+5)=7.5*5 \\ 3a+15=37.5 \\ by\text{ collecting like terms we will have that} \\ 3a=37.5-15 \\ 3a=22.5 \\ (3a)/(3)=(22.5)/(3) \\ a=7.5\operatorname{cm} \end{gathered}

Therefore XZ=XN+NZ


XZ=5+7.5=12.5\operatorname{cm}

To calculate YZ ,

We will use the pythagorean theorem,


\begin{gathered} XZ^2=YZ^2+XY^2 \\ 12.5^2=YZ^2+7.5^2 \\ 156.25=YZ^2+56.25 \\ YZ^2=156.25-56.25 \\ YZ^2=100 \\ YZ=\sqrt[]{100} \\ \vec{YZ}=10.0cm \end{gathered}

Therefore ,

The value of YZ is


\vec{YZ}=10.0\operatorname{cm}

Hence ,

The correct answer is OPTION B

In the figure shown MN is parallel to segment YZ what is the length of segment YZ-example-1
User Brodoll
by
7.7k points

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