In a right-angled triangle KMN, the angle K is straight, the height KE is 6, and EN = 8. Find KM, KN, ME, MN.
| January 30, 2021 | education
From the right-angled triangle NKE, we determine the length of the hypotenuse KN.
KN ^ 2 = NE ^ 2 + KE ^ 2 = 64 + 36 = 100.
KN = 10 cm.
Since the KE height is drawn from a right angle to the hypotenuse, KE2 = NE * ME, then ME = KE ^ 2 / NE = 36/8 = 4.5 cm.
From the right-angled triangle EKM we determine the length of the hypotenuse KM.
KM ^ 2 = KE ^ 2 + ME ^ 2 = 36 + 20.25 = 56.25.
KM = √56.25 = 7.5 cm.
Let us determine the length of the hypotenuse NM.
NM = NE + ME = 8 + 4.5 = 12.5 cm.
Answer: KM = 7.5 cm, KN = 10 cm, ME = 4.5 cm, MN = 12.5 cm.
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