PQRS is a parallelogram, S is the midpoint of line segment PT. Find the ratio of area of ΔPQR and area of ΔPQT.
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Given : PQRS is a parallelogram , S is the midpoint of line segment PT
To find : ratio of area of ΔPQR and area of ΔPQT.
Solution:
PQRS is a parallelogram , S is the midpoint of line segment PT
PR is diagonal hence area of ΔPQR = (1/2) area of parallelogram PQRS
Draw TM ⊥ PQ intersecting SR at N so TN ⊥ SR (∵PQ ║ SR)
Area of Δ PQT = (1/2) PQ * TM
in Δ TPM
SN is ║ PM
and S is mid point of PT
Hence N is mid point of TM ( Using BPT , thales theroem )
Hence TM = 2 * NM
Area of Δ PQT = (1/2) PQ * 2 * NM
Area of Δ PQT = PQ * NM
=> Area of Δ PQT = Area of parallelogram PQRS
area of ΔPQR = (1/2) area of parallelogram PQRS
=> area of ΔPQR = (1/2) Area of Δ PQT
=> area of ΔPQR / Area of Δ PQT = 1/2
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