Answer: 49
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Explanation:
HI is parallel to KL, so this means that the two triangles can be proven similar through the AA (angle angle) similarity theorem.
Consequently, that means we can set up the proportion below
JH/JK = HI/KL
noticed how the left slant sides JH and JK pair up together on one side; the horizontal sides HI and KL pair up on the other side. I have the larger triangle's side lengths as the numerator for each side
Plug in the given values. Solve for HI
JH/JK = HI/KL
35/15 = HI/21
7/3 = HI/21
21*7 = 3*HI
3*HI = 147
HI = 147/3
HI = 49
This means that 35/15 = HI/21 turns into 35/15 = 49/21
Note: to check the answer that the last equation mentioned is true, we can subtract the fraction 49/21 from both sides to end up with 35/15 - 49/21 = 0. If you type "35/15 - 49/21" into your calculator, you should get 0, which will help confirm we have the right answer.
