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?
Answers
Answer:
The triangles are congruent, and the areas are the same, but not the perimeters.
Step-by-step explanation:
ANSWER
(i) the triangles are congruent
△ABC≅△DEF
area(△ABC)=1×2+
2
1
×4=4sq. units
area(△DEF)=1×2+
2
1
×4=4sq. units
∴area(△ABC)=area(△DEF)
Thus, triangles are of equal areas and are congruent.
Perimeter:
As △ABC≅△DEF
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
△MNOnot≅△IJK
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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