Question

PQR is a triangle whose area is 180 sq.cm s is a point on side qr such that ps is the angle bisector

Answer 1

Answer:

Step-by-step explanation:

In a triangle PQR, PS is the angle bisector of ∠QPR and ∠QPS = 60°. What is the length of PS?

Area of a Δ = 1/2 × ac sinB = 1/2 × bc sinA = 1/2 × ab sinC (as the area of a triangle can be expressed using the lengths of two sides and the sine of the included angle).

∴ Area of ΔPQR = Area of ΔPQS + Area of ΔPSR

⇒ 1/2 × qr sin∠QPR = 1/2 × rs sin∠QPS + 1/2 × sq sin∠SPR (where s is the length of PS)

⇒ 1/2 × qr sin120° = 1/2 × rs sin60° + 1/2 × sq sin60° (as PS is bisector of ∠QPR and ∠QPS = 60°)

⇒ 1/2 × qr × √3/2 = 1/2 × rs × √3/2 + 1/2 × sq × √3/2

⇒ qr = rs + sq

⇒ s = qr/(q+r)