8. In 4ABC, A = 25
, B = 35
, and AB = 16 units. In 4PQR, P = 35
, Q = 120
, and PR = 4 units.
Which of the following is true?
(A) Area(4ABC) = 2 Area(4PQR)
(B) Area(4ABC) = 4 Area(4PQR)
(C) Area(4ABC) = 8 Area(4PQR)
(D) Area(4ABC) = 16 Area(4PQR)
Hi!
Here is the answer to your question.
Given, ∠A = 25°, ∠B = 35° and AB = 16
In ∆ABC,
∠A + ∠B + ∠C = 180°
⇒ 25° + 35° + ∠C = 180°
⇒ ∠C = 180° – 60° = 120°
Given, ∠P = 35°, ∠Q = 120° and PR = 4
In ∆PQR,
∠P + ∠Q + ∠R = 180°
⇒ 35° + 120° + ∠R = 180°
⇒ ∠R = 180° – 155° = 25°
Now, ∆ABC ∼ ∆RPQ (AA similarly)
The ratio of two similar triangles is equal to the ratio of the squares of any two corresponding sides.
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