In rectangle ABCD, AB = 10 cm and BC = 14 cm. If rectangle EFGH is the image after a dilation, which could be its side lengths?
1 answer:
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<h3>Answer: 125</h3>
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Explanation:
Ignore lines BC and FE. It might help to redraw the figure without those lines present. Refer to the diagram below. Doing this is optional if you can spot what's going on without having to erase those lines.
Notice how angles 1 and 3 are congruent corresponding angles, due to lines FJ and DC being parallel.
Since angle 3 is 55 degrees, angle 1 is also 55 degrees.
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Once we determine angle 1, we subtract from 180 because angle ABF is supplementary to angle 1 (aka angle ABJ)
In other words,
(angle ABJ) + (angle ABF) = 180
angle ABF = 180 - (angle ABJ)
angle ABF = 180 - (angle 1)
angle ABF = 180 - (55)
angle ABF = 125 degrees
The answer is x=4/3 and x=11/4
