Question

Nadine is making a quilt. She can use a rectangle of any length and width, as long as the angles in the shape are right angles. Which pieces of fabric can Nadine use in the quilt? Check all that apply.

Fabric 1
length: 5 cm
width: 12 cm
diagonal: 13 cm
Fabric 2
length: 8 cm
width: 6 cm
diagonal: 10 cm
Fabric 3
length: 4 cm
width: 5 cm
diagonal: 6 cm
Fabric 4
length: 10 cm
width: 8 cm
diagonal: 12 cm
Fabric 5
length: 6 cm
width: 4 cm
diagonal: 8 cm
Fabric 6
length: 8 cm
width: 15 cm
diagonal: 17 cm

Fabric 1
Fabric 2
Fabric 3
Fabric 4
Fabric 5
Fabric 6

Answer 1

The answer would be Fabric 6. To solve this problem, you would need to use the Pythagorean Theorem. 8² + 15² equals 17², which assures that the angles in the shape would be right angles.

Answer 2

Fabric 1, 2 and 6 can be used by Nadine.

Explanation:

When the diagonal and length and width are given, we can assume that if the sum of squares of length and width is equal to he square of diagonal, then it will be a right angle.

We will use Pythagoras theorem here:

`a^(2)+b^(2)=c^(2)`

We will check all the fabrics.

Fabric 1

length: 5 cm

width: 12 cm

diagonal: 13 cm

`5^(2) +12^(2) =13^(2)`

`25+144=169`

`169=169` (yes)

Fabric 2

length: 8 cm

width: 6 cm

diagonal: 10 cm

`8^(2) +6^(2) =10^(2)`

`64+36=100`

`100=100` (yes)

Fabric 3

length: 4 cm

width: 5 cm

diagonal: 6 cm

`4^(2) +5^(2) =6^(2)`

`16+25=36`

`41\\eq 36` (no)

Fabric 4

length: 10 cm

width: 8 cm

diagonal: 12 cm

`8^(2) +10^(2) =12^(2)`

`64+100=144`

`164\\eq 144` (no)

Fabric 5

length: 6 cm

width: 4 cm

diagonal: 8 cm

`4^(2) +6^(2) =8^(2)`

`16+36=64`

`52\\eq 64` (no)

Fabric 6

length: 8 cm

width: 15 cm

diagonal: 17 cm

`8^(2) +15^(2) =17^(2)`

`64+225=289`

`289=289` (yes)

Therefore, fabric 1, 2 and 6 can be used by Nadine.