In triangle pqr s is any point on pr such that ps:sr =2:3 , v is the point on qs such that qv:vs =1:3 if st is midian of triangle svr and area of triangle str - area of triangle qvt =12cm find area of pqr
Answers
Area of Δpqr = 160 cm²
Step-by-step explanation:
Area of Δ qvt = 12 cm²
st is median of Δ svr
=> t is mid point of vr
hence qt is median of Δ qvr
Hence Area of Δ qvt = (1/2)Area of Δ qvr
=> Area of Δ qvr = 2 * Area of Δ qvt
=> Area of Δ qvr = 2 * 12
=> Area of Δ qvr = 24 cm²
qv:vs=1:3
=> area of Δ qvr = (1/4) Area of Δqsr
=> Area of Δqsr = 4 * area of Δ qvr
=> Area of Δqsr = 4 * 24 = 96 cm²
ps:sr=2:3
=> Area of Δqsr = (3/5)* Area of Δpqr
=> Area of Δpqr = (5/3) * Area of Δqsr
=> Area of Δpqr = (5/3) * 96
=> Area of Δpqr = 160 cm²
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