Jonathan takes a piece of plywood that is 16 cm long and uses a table saw to make a 20 cm cut from a corner to its opposite corner. What was the breadth of the plywood?
Answers
Answer:
4 cm
Step-by-step explanation:
i think so.. is it correct?
Answer: To find a “fold” between two points, simply construct the perpendicular bisector between the points. To do this, join the points with a line, find the midpoint between the two points, and construct a perpendicular to that line through that point. If you do that with this 3cm by 4cm rectangle, the picture may look like this:
As you can see, the diagonal of the rectangle (which has length 5, since the diagonal creates the famous 3–4–5 right triangle) and the perpendicular bisector of that diagonal (also known as the Fold Line we need to find the length of) form two new smaller right triangles. I have outlined one of those triangles in red in my diagram. If we find x we can just double it to get the desired length.
The red triangle shares an angle with the 3–4–5 triangle and also has a right angle, so the red triangle is similar to the 3–4–5 triangle [by AA similarity]. Hence corresponding side have the same ratio:
(short leg of red triangle)/(short leg of 3–4–5 triangle)=(longer leg of red triangle)/(longer let of 3–4–5 triangle).
I have written this proportion above and solved it for x. Once you get x, just double it to get the length of the fold, which turns out to be 3.75 cm.
Step-by-step explanation:
