Question

Select all the sets of side lengths that will make a triangular shelf fit in a 90° corner of a room.
6 cm, 8 cm, 10 cm
2 cm, 3 cm, 4 cm
5 cm, 6 cm, 9 cm
3 cm, 4 cm, 5 cm
7 cm, 9 cm, 11 cm

Answer 1

formula to see if perfect right angle: A ² + B ² = C ²

1. 36 + 64 = 10 ² (100) YES

2. 4 + 9 = 4 ² (16) NO

3. 25 + 36 = 9 ² (81) NO

4. 9 + 16 = 5 ² (25) YES

5. 49 + 81 = 121 NO

The answers are:

1. 6cm, 8cm, 10cm
and
4. 7cm, 9cm, 11cm

Answer 2

The  sets of side lengths that will make a triangular shelf fit in a 90° corner of a room should be  6cm, 8cm, 10cm and 7cm, 9cm, 11cm

Calculation of the sets:

Since we know that

The Pythagoras theorem should be

$A^2 + B^2 = C^2$

So,

$6^2 + 8^2 = 10^2$

36 + 64 = 100

100 = 100

And,

$3^2 + 4^2 = 5^2$

9 + 16 = 25

25 = 25

Therefore, The  sets of side lengths that will make a triangular shelf fit in a 90° corner of a room should be  6cm, 8cm, 10cm and 7cm, 9cm, 11cm

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