Original
Next, we {{CMD_198}}find equations{{CMD_199}} that combine relevant
variables. In this case there are two. The first is the formula
for the area of a triangle:
{{MATH_200}}
The second uses the fact that the larger triangle is similar to
the smaller triangle, meaning that the ratios between the corresponding sides in both triangles
are equal,
{{MATH_201}}
At this point we could {{CMD_202}}differentiate{{CMD_203}} both equations, but we
choose a simpler path and express {{MATH_204}} in terms of {{MATH_205}}
{{ENV_206}}
Therefore,
{{MATH_207}}
Since {{MATH_208}} and {{MATH_209}} are both functions of time, we {{CMD_210}}differentiate{{CMD_211}} both sides of this equation with respect to {{MATH_212}}
{{MATH_213}}
In particular, when {{MATH_214}},
{{MATH_215}}
Hence, the area is changing at a rate of {{MATH_216}} {{MATH_217}} when {{MATH_218}}m.
{{CMD_219}}
{{CMD_220}}
{{CMD_221}}