SOLUTION: Draw a diagonal through cropped picture. Take length of diagonal (3 1/2") and extend it 3 more times on paper. Draw new rectangles with these new diagonal lengths amd measure the

Algebra ->  Sequences-and-series -> SOLUTION: Draw a diagonal through cropped picture. Take length of diagonal (3 1/2") and extend it 3 more times on paper. Draw new rectangles with these new diagonal lengths amd measure the      Log On


   

Question 713131: Draw a diagonal through cropped picture. Take length of diagonal (3 1/2") and extend it 3 more times on paper. Draw new rectangles with these new diagonal lengths amd measure the widths. What should I be noticing about these new widths? I need to write an arithmetic sequence that has the length of the original diagonal. Using the terms of sequence of diagonal lengths, find the corresponding picture widths. What would the new widths be? I am totally lost on this one.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
What was meant by "extend it 3 more times"?
Were you supposed to double, triple and quadruple the length of the diagonal?
Or were you supposed to make a 3%261%2F2inch diagonal longer by the same length each time? Maybe make it 4%261%2F2inch , 5%261%2F2inch , and 6%261%2F2inch , increasing the length by 1 inch each time?
In either case you are constructing similar right triangles. The sides of those triangles are the diagonal and the sides of each rectangle.
The ratio of lengths of side to diagonal are the same.
The diagonals are expected to form an arithmetic sequence.
(because you are adding the same length to the diagonal each time you extend it).
Since the ratio of side to diagonal is the same, the sides will also form an arithmetic sequence .

DOUBLING, TRIPLING AND QUADRUPLING:
(Easiest option, and maybe what the problem was about).
Your rectangle may not be like mine, but as you double the length of the diagonal you double the length of each side.
My diagonals measure 3.5, 7.0, 10.5, and 14.0 inches (increasing by 3.5" each time).
My rectangle lengths are 2.8, 5.6, 8.4, and 11.2 inches (increasing by 2.8" each time).
My rectangle widths are 2.1, 4.2, 6.3, and 8.4 inches (increasing by 2.1" each time).

ADDING 1 INCH TO THE DIAGONAL THREE TIMES:
Each time I add 1 inch to my diagonal (1%2F3.5=2%2F7 of the initial length), I am adding 0.8" (2.8%2A%282%2F7%29=0.8 inches) to the initial 2.8" length
and 0.6" (2.1%2A%282%2F7%29=0.6 inches) to the initial 2.1" width of the rectangle.
My diagonals measure 3.5, 4.5, 5.5, and 6.5 inches (increasing by 1.0" each time).
My rectangle lengths are 2.8, 3.6, 4.4, and 5.2 inches (increasing by 0 .8" each time).
My rectangle widths are 2.1, 2.7, 3.3, and 3.9 inches (increasing by 0.6" each time).