Question
Question
Luke is planning to lay two decorative pieces of wood across the 12-inch by 24-inch rectangular glass centerpiece of a cabinet. Each piece will lie on a diagonal of the centerpiece.
Select a number from the drop down menu to correctly complete the statement.
Each piece of wood should have a length of approximately
Choose...
inches.
Luke is planning to lay two decorative pieces of wood across the 12-inch by 24-inch rectangular glass centerpiece of a cabinet. Each piece will lie on a diagonal of the centerpiece.
Select a number from the drop down menu to correctly complete the statement.
Each piece of wood should have a length of approximately
Choose...
inches.
Answers
GPT-4o mini
To find the length of each piece of wood that lies on a diagonal of the rectangular centerpiece, we can use the Pythagorean theorem. The formula for the diagonal \( d \) of a rectangle can be expressed as:
\[
d = \sqrt{l^2 + w^2}
\]
where \( l \) is the length and \( w \) is the width of the rectangle.
In this case, the dimensions of the rectangular centerpiece are:
- Length \( l = 24 \) inches
- Width \( w = 12 \) inches
Now plug in the values:
\[
d = \sqrt{24^2 + 12^2}
\]
\[
d = \sqrt{576 + 144}
\]
\[
d = \sqrt{720}
\]
\[
d \approx 26.83 \text{ inches}
\]
Thus, each piece of wood should have a length of approximately **26.83** inches.
\[
d = \sqrt{l^2 + w^2}
\]
where \( l \) is the length and \( w \) is the width of the rectangle.
In this case, the dimensions of the rectangular centerpiece are:
- Length \( l = 24 \) inches
- Width \( w = 12 \) inches
Now plug in the values:
\[
d = \sqrt{24^2 + 12^2}
\]
\[
d = \sqrt{576 + 144}
\]
\[
d = \sqrt{720}
\]
\[
d \approx 26.83 \text{ inches}
\]
Thus, each piece of wood should have a length of approximately **26.83** inches.