Answer:
The answer is 28
Step-by-step explanation:
15 divided by 10 is 1.5,
42 divided by 1.5 equals 28,
hence the answer is 28.
Answer: x = 28 unit
Step-by-step explanation:
Here, In triangle APR,
CD ║ AP,
Such that, C ∈ AR and D ∈ PR,
Also, AC = 10 unit, CR = x unit, PD = 15 unit and DR = 42 unit,
Since, CD ║ AP,
Thus, by the alternative interior angle theorem,
[tex]\angle APR\cong \angle CDR[/tex]
[tex]\angle PAR\cong \angle DCR[/tex]
Thus, By AA similarity postulate,
[tex]\triangle APR\sim \triangle CDR[/tex]
Since, the corresponding sides of the similar triangle are in same proportion,
[tex]\implies \frac{AR}{CR}=\frac{PR}{DR}[/tex]
[tex]\implies \frac{AC+CR}{CR}=\frac{PD+DR}{DR}[/tex]
[tex]\implies \frac{10+x}{x}=\frac{15+42}{42}[/tex]
[tex]\implies 420 + 42 x = 15 x + 42 x[/tex]
[tex]\implies 420 = 57 x - 42 x[/tex]
[tex]\implies 420 = 15 x\implies 28 = x[/tex]
Hence, the value of x = 28.
