Question

If YZ = t + 83 and VX = t + 39, what is YZ?

Answer 1

The given expressions are

`\begin{gathered} YZ=t+83 \\ VX=t+39 \end{gathered}`

Let the value of

`\begin{gathered} WX=a \\ YX=a \\ YW=WX+YX=a+a=2a \end{gathered}`

Concept:

We will apply the rule of simolar triangles given below as

`(WX)/(YW)=(VX)/(ZY)`

By Substituting the values, we will have

`\begin{gathered} (WX)/(YW)=(VX)/(ZY) \\ (a)/(2a)=(t+39)/(t+83) \\ (1)/(2)=(t+39)/(t+83) \\ cross\text{ multiply, we will have} \\ t+83=2\left(t+39\right) \\ t+83=2t+78 \\ collect\text{ similar terms,} \\ 2t-t=83-78 \\ t=5 \end{gathered}`

To calculate the value of YZ, we will susbtitute the value of t=5 in the equation below

`\begin{gathered} YZ=t+83 \\ YZ=5+83 \\ YZ=88 \end{gathered}`

Hence,

The value of YZ = 88