# Question

Dear all,

I did not understand, how the ratio of triangle MOQ to MON is same as that of QOP to NOP? ( I did not follow the logic in the step in 3rd line from las)t. Any expert help please ?

Basically because the triangles share the same bases.

Note : the “H” and “h” is for illustration purpose only. It may not be the “correct” height of the triangles when computing the area.

Thanks Acestarling,

May I double confirm again. Since the bases are same and only height differs, area of MOQ and QOP are different (& represent the height ratio). But the, area of OMQ:area of OMN = area of QOP:area of OPN (as the bases are same & the height difference is accounted by the difference in the exact value of area we get)

hi, ksraja69

What you say is correct.

Area MOQ is not equal to Area QOP.

Area MON is not equal to Area NOP.

But in terms of ratio comparison with respect to each other,

MOQ : MON  =  QOP : NOP

as the triangle height becomes insignificant.

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Perhaps you may like to consider this as another alternative method if you do not want to use the “equivalent ratio” relation as provided in the key solution.

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