# 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!

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.
Cheers!

• 1

d)area of tri. ABC = 16 * area of tri. PQR .......

• 2

coz tri. ABC and tri. PQR r similar ..... as all angels r equal ....

accordin to area theorem :-

area of ABC / area of PQR = AB2 / PR2

----> area of ABC / area of PQR = 256 / 16

----> area of ABC / area of PQR = 16

----> area of ABC = 16 * area of PQR ..

Hope this helps !!

• 0
What are you looking for?