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?

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?

Answer 1

Here, $△ A B C ≅ △ D E F$
$∴ a r (A B C) = 2 + 2 = 4$ sq.units
$a r (D E F) = 2 + 2 = 4$ sq.units
$∴ a r (A B C) = a r (D E F)$
Thus, Triangle are of equal areas and are congruent
Now, To check perimeter of both triangles,
As $△ A B C ≅ △ D E F$
By $C P C T$
$A B = D E$
$B C = E F$
$A C = D F$
$∴$ By adding,
$A B + B C + A C = D E + E F + D F$
$∴$ Perimeter of $△ A B C$ = Perimeter of $△ D E F$
$∴$ Perimeter of congruent triangle are also equal.

Answer 2

Here,

△ A B C ≅ △ D E F

∴ a r (A B C) = 2 + 2 = 4

sq.units

a r (D E F) = 2 + 2 = 4

sq.units

∴ a r (A B C) = a r (D E F)

Thus, Triangle are of equal areas and are congruent

Now, To check perimeter of both triangles,

As

△ A B C ≅ △ D E F

By

C P C T

A B = D E

B C = E F

A C = D F

∴

By adding,

A B + B C + A C = D E + E F + D F

∴

Perimeter of

△ A B C

= Perimeter of

△ D E F

∴

Perimeter of congruent triangle are also equal.

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

Answer

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False

Answer

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