*see attachement for the triangles given
Answer:
PQ = 6.8
Step-by-step explanation:
Corresponding sides of similar shapes or figures are proportional to each other. Since ∆LMN ~ ∆OPQ, the ratio of their corresponding sides would therefore be equal. Thus:
LN/OQ = MN/PQ
LN = 5
OQ = 17
MN = 2
PQ = ?
Plug in the values
5/17 = 2/PQ
Cross multiply
5*PQ = 2*17
5*PQ = 34
PQ = 34/5
PQ = 6.8
Answer:
The required value of x = 3
Step-by-step explanation:
For better understanding of the solution, see the attached figure :
The given three points are collinear to each other and the point P lies somewhere between the end points of the line MN
So, to find the value of x we can use the relation : Sum of Mid segments PM and PN is equal to complete length of the line segment MN
⇒ PN + PM = MN
⇒ 6·x + 2·x - 5 = 5·x + 4
⇒ 8·x - 5·x = 4 + 5
⇒ 3·x = 9
⇒ x = 3
Hence, The required value of x = 3
