Question

PQR is a triangle with PQ = 15, QR = 25, RP-30, A, B are points on PQ and PR respectively such that <PBA= <PQR" The perimeter of the triangle PAB is 28, then the length of AB is

a.8
b.10
c.12
d.25/6

please provide the answer with explanation or solution ​

Answer 1

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Answer 2

Given :- In ∆PQR , PQ = 15, QR = 25, RP-30, A, B are points on PQ and PR respectively such that ∠PBA = ∠PQR . The perimeter of the triangle PAB is 28 .

To Find :- The length of AB is :-

A) 8

B) 10

C) 12

D) 25/6

Solution :-

In ∆PBA and ∆PQR we have,

→ ∠PBA = ∠PQR

since corresponding angles are equal . We know that, if corresponding angles are equal, then the lines are parallel to each other . we can say that the two lines BA and QR are parallel to each other.

So,

→ ∠PAB = ∠PRQ { Corresponding angles }

then,

→ ∆PBA ~ ∆PQR { By AA similarity }

therefore,

→ PB/PQ = PA/PR = BA/QR = Perimeter ∆PBA / Perimeter ∆PQR { When two ∆'s are similar their corresponding side and their perimeter are in the same ratio . }

hence,

→ BA/QR = Perimeter ∆PBA / Perimeter ∆PQR

→ BA/25 = 28 / (15 + 25 + 30)

→ BA/25 = 28/70

→ BA/25 = 2/5

→ 5•BA = 25 × 2

→ BA = 5 × 2

→ BA = 10 (Ans.)

∴ The length of AB is equal to Option (b) 10 units .

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