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Question

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?

  1. True
  2. False

A
True
B
False
Solution
Verified by Toppr

Two congruent triangles
Here, ΔABCΔDEF
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 ΔABCΔDEF
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.

1061461_705195_ans_8808b6318bf746e0913edfb16fcee73a.png

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