Question

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

Answer 1

Answer: Option (2) is correct.

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 :

`KL^2=KN.KM-----(1)\\\\ML^2=MN.KM-------(20\\\\LN^2=KN.MN------(3)`

So, According to the options ,

Put LM = 12, NM = 9,

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

Since, it satisfies that KLM is a right triangle.

Hence, Option (2) is correct.