In a squared sheet, draw two triangles of equal areas such that (i) the triangles are congruent. (ii) the triangles are not congruent. Will their perimeters be the same?
True
False
A
True
B
False
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Solution
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Two congruent triangles
Here, ΔABC≅ΔDEF
∴ar(ABC)=2+2=4 sq. units
ar(DEF)=2+2=4 sq. units
∴ar(ABC)=ar(DEF)
Thus, triangles are of equal areas and are congruent
Now,
To check perimeter of both triangles,
As ΔABC≅ΔDEF
By CPCT
AB=DE
BC=EF
AC=DF
∴ By adding,
AB+BC+AC=DE+EF+DF
∴ Perimeter of ΔABC=Perimeter of ΔDEF
Thus, perimeter of congruent triangles are also equal.
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