Question

A teacher asks her students to design a game board for a class project. The dimensions of the boards created by four students are shown below.

Angela
length: 20 cm
width: 21 cm
diagonal: 29 cm
Bradley
length: 9 in.
width: 9 in.
diagonal: 9 in.
Carlton
length: 25 cm
width: 30 cm
diagonal: 35 cm
Della
length: 10 in.
width: 12 in.
diagonal: 15 in.

Whose game board could be a rectangle?
Angela
Bradley
Carlton
Della

Answer 1

To determine whose game board could be a rectangle, we need to check if the dimensions given for each student's board satisfy the properties of a rectangle, specifically the Pythagorean theorem. A rectangle's diagonal can be calculated using the formula:

\[
d = \sqrt{l^2 + w^2}
\]

where \(d\) is the diagonal, \(l\) is the length, and \(w\) is the width.

**Angela:**
- Length: 20 cm
- Width: 21 cm
- Diagonal: 29 cm

Calculating the diagonal:
\[
d = \sqrt{20^2 + 21^2} = \sqrt{400 + 441} = \sqrt{841} = 29 \text{ cm}
\]
This satisfies the rectangle condition.

**Bradley:**
- Length: 9 in.
- Width: 9 in.
- Diagonal: 9 in.

Calculating the diagonal:
\[
d = \sqrt{9^2 + 9^2} = \sqrt{81 + 81} = \sqrt{162} \approx 12.73 \text{ in}
\]
This does not satisfy the rectangle condition.

**Carlton:**
- Length: 25 cm
- Width: 30 cm
- Diagonal: 35 cm

Calculating the diagonal:
\[
d = \sqrt{25^2 + 30^2} = \sqrt{625 + 900} = \sqrt{1525} \approx 39.05 \text{ cm}
\]
This does not satisfy the rectangle condition.

**Della:**
- Length: 10 in.
- Width: 12 in.
- Diagonal: 15 in.

Calculating the diagonal:
\[
d = \sqrt{10^2 + 12^2} = \sqrt{100 + 144} = \sqrt{244} \approx 15.62 \text{ in}
\]
This does not satisfy the rectangle condition.

**Conclusion:**
Only **Angela's** game board could be a rectangle.