Question

Please, answer this one. Thank you! ​

Answer 1

3

Explanation:

Since LM = 9 and ST = 6 and those are corresponding sides, the ratio of any side from
`\triangle{PLM}` and its corresponding side from
`\triangle{UST}` is 9 to 6 which can be expressed as the fraction 9/6 or 3/2.

LQ and SR are corresponding segments, so set up two ratios.

`(LQ)/(SR)=(3)/(2)\\\\(x-1)/(x-2)=\frac{3}2}`

Now "cross-multiply" (using what you may have seen called the Means-Extremes Property).

`2(x-1)=3(x-2)\\\\2x-2=3x-6\\\\4=x`

Now put in 4 for x in the expression for LQ.

`LQ=x-1=4-1=3`