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?

Answer 1

Answer:

Step-by-step explanation:

(i) Here,

ΔABC ≅ ΔDEF

For Triangle ABC,

1. No. of boxes = 2

Area = 1 × 2 = 2

2. No. of boxes = 4

Area = 1/2 × 4 = 2

Therefore, ABC 2 + 2 = 4 square units

For Triangle DEF,

1. No. of boxes = 2

Area = 1 × 2 = 2

2. No. of boxes = 4

Area = 1/2 × 4 = 2

(ii) Here,

ΔABC is not congruent to ΔDEF.

For Triangle ABC,

1. No. of boxes = 2

Area = 1 × 2 = 2

2. No. of boxes = 2

Area = 1 × 2 = 2

3. No. of boxes = 3

Area = 0 × 3 = 0

Therefore, ABC = 2 + 2

For Triangle DEF,

1. No. of boxes = 2

Area = 1 × 2 = 2

2. No. of boxes = 2

Area = 1 × 2 = 2

3. No. of boxes = 2

Area = 0 × 2 = 0

Therefore, DEF = 2 + 2 + 2 = 6 square units.

So they are not congruent.

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