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lisov135 [29]
3 years ago
6

In △ABC, point M is the midpoint of AB , point D∈ AC so that AD:DC=2:5. If AABC=56 yd2, find ABMC, AAMD, and ACMD.

Mathematics
1 answer:
Natasha2012 [34]3 years ago
4 0

Answer: The area of BMC is 28 yd square, the area of AMD is 8 yd square and the area of CMD is 20 yd square.

Explanation:

It is given that the M is the midpoint of the side AB. The line MC is the median of the triangle ABC.

A median divides the area of triangle in two equal parts, therefore the area of triangle BMC is half of the area of triangle ABC.

\text{ Area of }\triangle BMC =\frac{1}{2}\times \text{ Area of }\triangle ABC}

\text{ Area of }\triangle BMC =\frac{1}{2}\times 56}

\text{ Area of }\triangle BMC =28

Therefore the area of BMC and AMC is 28 yd square.

Draw a perpendicular on AD from M as shown in the figure.

\frac{\text{ Area of }\triangle AMD}{\text{ Area of }\triangle AMC}= \frac{\frac{1}{2}\times AD\times ME}{\frac{1}{2}\times AC\times ME} =\frac{AD}{AC}= \frac{2}{7}

Therefore the area of AMD is  \frac{2}{7}th  part of the area of AMC.

\text{ Area of }\triangle AMD =\frac{2}{7}\times \text{ Area of }\triangle AMC}

\text{ Area of }\triangle AMD =\frac{2}{7}\times 28

\text{ Area of }\triangle AMD =8

Therefore the area of AMD is 8 yd square.

\text{ Area of }\triangle CMD=\text{ Area of }\triangle ABC-\text{ Area of }\triangle AMD-\text{ Area of }\triangle BMC

\text{ Area of }\triangle CMD=56-8-28=20

Therefore the area of CMD is 20 yd square.

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