Rectangles A and B are similar rectangles. The length of the diagonal of Rectangle A is 13 inches and the length of the diagonal of Rectangle B is 6.5 inches.

What could be the length and width of both Rectangle A and Rectangle B? Show your work.

Rectangle A: 5 in x 12 in, Rectangle B: 2.5 in x 6 in

Rectangle A: 6.5 in x 14 in, Rectangle B: 3.5 in x 8 in
Rectangle A: 4 in x 10 in, Rectangle B: 3 in x 7 in

Rectangle A: 7 in x 11 in, Rectangle B: 2 in x 5 in

Question

Rectangles A and B are similar rectangles. The length of the diagonal of Rectangle A is 13 inches and the length of the diagonal of Rectangle B is 6.5 inches. 
  
What could be the length and width of both Rectangle A and Rectangle B? Show your work.

 Rectangle A: 5 in x 12 in, Rectangle B: 2.5 in x 6 in

 Rectangle A: 6.5 in x 14 in, Rectangle B: 3.5 in x 8 in
 Rectangle A: 4 in x 10 in, Rectangle B: 3 in x 7 in

 Rectangle A: 7 in x 11 in, Rectangle B: 2 in x 5 in

anonymous · Answer

You could use the Pythagoras theorem for this. Since a rectangle is made up of 2 triangles, take the diagonals to be the longest side of the triangle. The ratio 5:12:13 for the sides of the right angle triangle fits the equation $$a ^{2} + b ^{2} = c ^{2}$$, so for Rectangle A, the width and length could be 5in and 12in. For Rectangle B, the long side is 6.5in, which is just 13/2, so you divide the other lengths by 2 to get 2.5in and 6in.

anonymous · Answer

your name skips 6... (: