Janenett R.

# Triangle ABC is a right triangle with the side lengths shown. What is the length of BC?

Since i cant show the actual triangle i hope it will help if i mention that line BA of the triangle is 5 and so is line AC
A) 2√5
B) 5√2
C) 10
D) 25
I beileve its B but im not sure how to explain it

## 2 Answers By Expert Tutors

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Michael J.

How do you know 5 is not the hypotenuse?
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08/18/15 Faith H.

The hypotenuse is always the longest side of a right triangle.  Since both of the given sides=5, we know that neither of them can be the hypotenuse.
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08/18/15

Michael J.

Suppose we had a triangle with side lengths of 3 and 5.  Then 5 cannot be one of the legs because the right triangle follows 3,4,5 triple rule.   Since 5 is the longest side c, then the hypotenuse would have to be 5, and the two legs a and would be 3 and 4.  You are fortunate that in this triangle, 5 is both the legs. But not all triangles will be like the one in this problem.
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08/18/15 David W.

tutor
Note, by elimination:  For every kind of triangle, the sum of the lengths of any two sides must be larger than the third side.  Thus, distractors C (with 5,5,10) and D (with 5,5,25) cannot make a triangle at all.  The triangle formed by distractor (A) is not a right triangle because no combination of the squares of 5 and 5 [that is, 25 and 25] and the square of 2*SQRT(5) [that is, 20] can fit the form of A^2 + B^2 = C^2 that is true of a right triangle.  This is true, however, for distractor B [with squares of 25, 25, and 50].

For many, many problems in math (Algebra, Trigonometry, Calculus). engineering, and other disciplines -- on homework and on tests -- the "famous right triangles" include:
N           N          N*SQRT(2)             angles of   45, 45, 90
N     N*SQRT(3)        2*N                 angles of  30, 60, 90
3*N       4*N              5*N                 (learn in trig)

Knowing the squares of the first several numbers (1,4,9,16,25,36,...) and the differences and sums of the these squares will help with a whole lot math problems!
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08/18/15 David W.

tutor
Note to Michael J.:  Sometimes, question writers trick us by using the right triangle [3, 5, SQRT(34)] which indeed does have legs of length 3 and 5.  So, don't assume that 5 isn't one of the legs.
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08/18/15 Faith H.

Because of the information given, we know two key pieces of information about this triangle: one, that it is a right triangle; two, there are two sides with lengths of 5.  Because the hypotenuse is always the longest side of a right triangle, we know that the missing value is the hypotenuse (as the two remaining side lengths are equal).  Because of the side lengths we are given, we know that the 3, 4, 5 rule does not apply.

The important thing to remember when working on problems such as this is the relationship between the parts of a right triangle and the Pythagorean Theorem.  With a grasp on those concepts, one can solve any such problem.
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08/18/15

Janenett R.

thank you very much!
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08/18/15

Tutor
5 (5)

Understanding all Sines of Triangles

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