# In triangle pqr ,base qr is divided at x such that qx=1/2xr.prove that ar triangle pqx =1/3ar triangle per

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by ysnavneeth16

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by ysnavneeth16

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X divides the base QR in the ratio of 2:1 i.e., QX= 1/2 XR

rtp: ar triangle PQX =1/3ar triangle PQR

construction: join PX

draw an altitude PY for triangle PQR

proof: area of triangle PQX = 1/2 *PY*QX

area of triangle PXR = 1/2 * PY * XR

= 1/2 * PY * 2QX

= 2(1/2 * PY * QX)

= 2( area of triangle PQX)

we know that, area of triangle PQR = area of triangle PQX + area of triangle PXR

= 3( area of triangle PQX)

area of triangle PQX = 1/3(area of triangle PQR )

hence proved