In the triangle PQR, S is the midpoint of QR. X is any point on PR. T is the point on QR such that PT‖SX. If the area of triangle PQR is 5.8 sq. cm, then the area of triangle RTX is
Explanation:
Since S is the midpoint of QR, A(∆PSR)
= A(∆PQR)/2
= 5.8/2 = 2.9 sq.cm
Now A(∆PSR) = A(∆PSX) + A(∆SXR)
Also, A(∆RTX) = A(∆TSX) + A(∆SXR)
Now, triangles PSX and TSX lie within the same parallel lines – SX and PT – and hence, have the same area.
∴ A(∆PSX) = A(∆TSX)
∴ A(∆PSR) = A(∆RTX) = 2.9 sq.cm
Hence, option (a).
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