Caleb A.

asked • 09/17/20

HJ=4x+9, JK=3x+3, KH=33

i need help finding x, HJ, JK

Tracy D.

Is there a drawing to go with this, or perhaps J is the midpoint to HK or something?
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09/17/20

Doug V.

Caleb, we would need to know the relationship among the points H, J, and K. Are they collinear (all on one line)? If so, which point is between the other two? If they are not collinear, they would form a triangle. If that's the case, do we know anything special about the triangle, such as congruent sides or congruent angles?
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09/17/20

2 Answers By Expert Tutors

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Elad S. answered • 09/17/20

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We can see here that we have a triangle. One very important rule with a triangle is that no 2 sides can be shorter than the third side. In other words, looking at this problem: HJ + JK > KH, KH + JK > HJ, and HJ + KH > JK. Therefore, we can use algebra to solve for x:

HJ + JK > KH

  1. Replace the lengths with their lengths

(4x + 9) + (3x +3) > 33

4x + 9+ 3x + 3 > 33

(4x + 3x) + (9 + 3) > 33

7x + 12 > 33

(-12) + 7x + 12 > 33 + (-12)

7x > 21

7x/7 > 21/7

x > 3


This is your answer, in order for the triangle to be real and work, x has to be any value greater than 3.

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Elad S.

Now knowing that x > 3 HJ > 4(3) + 9 HJ > 21 JK > 3(3) + 3 JK > 12
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09/17/20

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