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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]  26 Nov 2017, 06:57
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Question Stats:

62% (01:18) correct 37% (00:39) wrong based on 16 sessions
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

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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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Expert's post
Look at the figure below:

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 [ 13.28 KiB | Viewed 4735 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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