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Kirstie is testing values that would make triangle klm a right triangle when ln is an altitude, and km = 16, as shown below. which lengths would make triangle klm a right triangle? 1) lm = 13 and kn = 6 2) lm = 12 and nm = 9 3) kl = 11 and kn = 7 4) ln = 8 and nm = 10

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MrsWilliams18
The Pythagorean Theorem is one that proves a right triangle is truly a right triangle. By plugging in our sides, we can determine whether or not a triangle is a right triangle. We know that the pythagorean theorem is written as follows: 

[tex] a^{2} [/tex] + [tex] b^{2} [/tex] = [tex] c^{2} [/tex]

After drawing the representation of the triangle, and using side km = 16, we can use the process of elimination to determine which answer choice will give us a balanced equation (both sides of the equation are equal to each other). When we plug lm = 12 and nm = 9 into our equation, we have the following: 

[tex] 12^{2} [/tex] = 9 * 16

144 = 144

So, the lengths that would make triangle klm a right triangle are lm = 12 and nm = 9. 

Answer:  Option (2) is correct.

Step-by-step explanation:

Since we have given that

KLM is a right triangle, in which KM = 15, and ln is an altitude.

As we know that for right angled triangle, there are 3 conditions :

[tex]KL^2=KN.KM-----(1)\\\\ML^2=MN.KM-------(20\\\\LN^2=KN.MN------(3)[/tex]

So, According to the options ,

Put LM = 12, NM = 9,

[tex]\text{Using eq. (3), we have}\\\\LN^2=KM.MN\\\\12^2=9\TIMES 16\\\\144=144[/tex]

Since, it satisfies that KLM is a right triangle.

Hence, Option (2) is correct.

Ver imagen RenatoMattice

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