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2025 VIMC keystage2-EMIC team Question 5

xIMC · 2025 VIMC keystage2-EMIC team

Question 5

In the diagram below, $ABCD$ is a quadrilateral of area $675$ cm², where $AB$ and $CD$ are parallel and $AB=20$ cm, $CD=25$ cm. Points $M,R$ and $T$ are on segments $BD,AB$ and $AC$, respectively, such that $\frac{MD}{MB}=\frac16$ and $\frac{TC}{TA}=\frac14$.

If the area of the triangle $MRT$ is $216$ cm², what is the length, in cm, of $AR$?

Question illustration