Points $A,B,C$ lie on the same straight line, with $AB=4\text{ cm}$ and $BC=6\text{ cm}$. Tria

Question

Points $A,B,C$ lie on the same straight line, with $AB=4\text{ cm}$ and $BC=6\text{ cm}$. Triangles $ADB$ and $BDC$ share vertex $D$. The area of triangle $ADB$ is $10\text{ cm}^2$. Find the area of triangle $BDC$.[2] Explain why squaring the base ratio $4:6$ would be incorrect here.[1]

Accepted Answer

(a) $15\text{ cm}^2$. (b) Equal heights give the base ratio directly; similarity is not given.

Triangles with a common height

Triangles with a common height

Solution:

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