Question

I have a test tomorrow and this is the review I don’t understand this.Question 4

Answer 1

Step-by-step explanation

From the statement, we know that triangles ΔLJK and ΔOMN. From the picture, we see that:

• sides LJ = 6 in and OM = 4 in are similar,

,

• sides JK = 9 in and MN = 6 in are similar,

,

• sides KL = 15 in and NO = x are similar.

From geometry, we know that two triangles are similar if they have the same ratio of corresponding sides and equal pairs of corresponding angles.

Taking into account this, we have:

`r=(LJ)/(OM)=(KL)/(NO).`

Replacing the data from above, we have:

`\begin{gathered} \frac{6\text{ }in}{4\text{ }in}=\frac{15\text{ }in}{x}, \\ (6)/(4)=\frac{15\text{ }in}{x}. \end{gathered}`

Solving this equation for x, we get:

`\begin{gathered} x\cdot(6)/(4)=15\text{ }in, \\ x=(4)/(6)\cdot15\text{ }in, \\ x=10\text{ }in. \end{gathered}`Answer

x = 10 in