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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
What can you say about their perimeters?

Solution
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(i) the triangles are congruent

ABCDEF

area(ABC)=1×2+12×4=4sq. units

area(DEF)=1×2+12×4=4sq. units

area(ABC)=area(DEF)

Thus, triangles are of equal areas and are congruent.

Perimeter:

As ABCDEF

By CPCT

AB=DE
BC=EF
AC=DF

Adding all the above 3, we get,

AB+BC+CA=DE+EF+FD

Perimeter of ABC = Perimeter of DEF

Thus, perimeters of congruent triangles are also equal.

(ii) the triangles are not congruent

MNOnotIJK

area(MNO)=1×2+1×2=4sq. units

area(IJK)=1×2+1×2=4sq. units

area(MNO)=area(IJK)

Thus, triangles are of equal areas and are congruent.

Perimeter:

Perimeter of MNO = Perimeter of IJK

Thus, perimeters of triangles are not equal.

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