Ex 7.2, 7 In a squared sheet, draw two triangles of equal areas such that (i) the triangles are congruent. What can you say about their perimeters?Two congruent triangles
Here,
∆ABC ≅ ∆DEF
Finding ar (ABC)
∴ ar (ABC) = 2 + 2
= 4 square units
Finding ar (DEF)
∴ ar (DEF) = 2 + 2
= 4 square units
∴ ar (ABC) = ar (DEF)
Thus, triangles are of equal areas and are congruent
Now,
Let’s check perimeter of both triangles
As Δ ABC ≅ Δ DEF
By CPCT
AB = DE
BC = EF
AC = DF
Adding (1), (2) & (3)
AB + BC + AC = DE + EF + DF
Perimeter of Δ ABC = Perimeter of Δ DEF
Thus, perimeters of congruent triangles are also equal
Ex 7.2, 7 In a squared sheet, draw two triangles of equal areas such that (ii) the triangles are not congruent. What can you say about their perimeters?
Two triangles not congruent
Here,
∆MNO ≇ ∆IJK
Finding ar (MNO)
∴ ar (MNO) = 2 + 2
= 4 square units
Finding ar (IJK)
∴ ar (IJK) = 2 + 2
= 4 square units
Thus,
ar (MNO) = ar (IJK)
But ∆MNO ≇ ∆IJK
Measuring Perimeter
By measuring Perimeter,
Perimeter of MNO > Perimeter of IJK
So, Perimeter are not equal.

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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