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In triangle ABC, the measure of angle B is 90°, the length o

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In triangle ABC, the measure of angle B is 90°, the length o [#permalink] New post 26 Nov 2017, 06:57
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In triangle ABC, the measure of angle B is 90°, the length of side AB is 4, and the length of side BC is x. If the length of hypotenuse AC is between 4 and 8, which of the following could be the value of x ?

Indicate \(all\) such values.

❑ 1

❑ 2

❑ 3

❑ 4

❑ 5

❑ 6

[Reveal] Spoiler: OA
A,B,C,D,E,F
[Reveal] Spoiler: OA

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Re: In triangle ABC, the measure of angle B is 90°, the length o [#permalink] New post 27 Nov 2017, 16:46
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Look at the figure below:

Image

Length of side AB is 4, and the length of side BC is xand AC is between 4 and 8. There can be many triangles that satify this condition.

On one extreme when AC is almost 4. Then the the triangle becomes almost the line AB and \(x\) is almost 0.
On the other hand when AC is 8 then \(x=\sqrt{8^2-4^2} \approx 6.9\).

So all values from 0 to 6.9 form a right triangle. Hence all options are correct!


[Reveal] Spoiler: img
Attachment:
right.jpg
right.jpg [ 13.28 KiB | Viewed 3541 times ]

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Re: In triangle ABC, the measure of angle B is 90°, the length o   [#permalink] 27 Nov 2017, 16:46
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In triangle ABC, the measure of angle B is 90°, the length o

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