Question

if A(triangle ABC)=32 sq units and A(triangle ADC)=12 sq units,then find BD?
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Answer 1

Answer:

Step-by-step explanation:

First we draw a triangle ABC with median AD , and midpoint G of AD .

Now we can show that each of the 4 smaller triangles have the same area.

△AGC has base AG=12AD , and height = altitude from C to AD

△DGC has base DG=12AD , and height = altitude from C to AD

Area (△DGC)= Area (△AGC)=32

Area (△ACD)=2∗32=64

△ABD has base BD=12BC , and height = altitude from A to BC

△ACD has base CD=12BC , and height = altitude from A to BC

Area (△ABD)= Area (△ACD)=64

△AGB has base AG=12AD , and height = altitude from B to AD

△DGB has base DG=12AD , and height = altitude from B to AC

Area (△AGB)= Area (△DGB)=12⋅64=32

Area (△BGC)= Area (△DGB)+ Area (△DGC)=64