Question
Domenica plans to divide a rectangular board into two congruent right triangles for use in an art project. The board is shown below.
A rectangle 16 units long and 12 units wide is divided diagonally into two right triangles by a dotted line. Diagonal length is labeled with a question mark.
What is the length of the diagonal cut she must make to divide the board?
A.
10 inches
B.
inches
C.
20 inches
D.
28 inches
A rectangle 16 units long and 12 units wide is divided diagonally into two right triangles by a dotted line. Diagonal length is labeled with a question mark.
What is the length of the diagonal cut she must make to divide the board?
A.
10 inches
B.
inches
C.
20 inches
D.
28 inches
Answers
GPT-4o mini
To find the length of the diagonal that divides a rectangle into two congruent right triangles, we can use the Pythagorean theorem.
In this case, the rectangle has a length of 16 units and a width of 12 units. The diagonal \(d\) can be calculated using the formula:
\[
d = \sqrt{(length^2) + (width^2)}
\]
Substituting the given dimensions:
\[
d = \sqrt{(16^2) + (12^2)}
\]
\[
d = \sqrt{(256) + (144)}
\]
\[
d = \sqrt{400}
\]
\[
d = 20
\]
Therefore, the length of the diagonal cut she must make to divide the board is:
C. 20 inches
In this case, the rectangle has a length of 16 units and a width of 12 units. The diagonal \(d\) can be calculated using the formula:
\[
d = \sqrt{(length^2) + (width^2)}
\]
Substituting the given dimensions:
\[
d = \sqrt{(16^2) + (12^2)}
\]
\[
d = \sqrt{(256) + (144)}
\]
\[
d = \sqrt{400}
\]
\[
d = 20
\]
Therefore, the length of the diagonal cut she must make to divide the board is:
C. 20 inches