Domenica plans to divide a rectangular board into two congruent right triangles for use in an art project. The board is shown below.

Question

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

Answer 1

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