Answer:
x = 67.50 ft
Step-by-step explanation:
Consider, ΔMAB and ΔMNP,
∠M = ∠M (Common)
Given AB║NP and let MN as transversal,
∠MAB = ∠MNP (alternate angle)
Also, Given AB║NP and let MP as transversal,
∠MBA = ∠MPN (alternate angle)
Therefore, ΔMAB ≅ ΔMNP (By AAA similarity )
Thus, by CPCT,
[tex]\frac{MA}{MN}=\frac{MB}{MP}=\frac{AB}{NP}[/tex]
consider first two ratios,
[tex]\frac{MA}{MN}=\frac{MB}{MP}[/tex]
Substitute the values, MA = MN - AN = 49.5 ft
[tex]\frac{49.5}{71.5}=\frac{x}{97.5}[/tex]
On solving for x , we get, x = 67.50 ft
Thus, value of x is 67.50 ft
