Question

What is the value of x?

Enter your answer, as a decimal, in the box.

Answer 1

22/71.5 = 4/13
BP = 97.5 * 4/13
BP = 30
MB = MP - BP
MB = 67.5 ft

Answer 2

x = 67.50 ft

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,

`(MA)/(MN)=(MB)/(MP)=(AB)/(NP)`

consider first two ratios,

`(MA)/(MN)=(MB)/(MP)`

Substitute the values, MA = MN - AN = 49.5 ft

`(49.5)/(71.5)=(x)/(97.5)`

On solving for x , we get, x = 67.50 ft

Thus, value of x is 67.50 ft