Question

Отношение отрезков MN и МК равно 6 : 8. Найдите: a) MN : NK; б) NK : MN; в) MK : MN.

Answer 1

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Answer 2

Given Information:

The ratio of the lengths of segments MN and MK is 6:8.

Solution:

To find the ratios MN:NK, NK:MN, and MK:MN, we need to divide the given ratio 6:8 into its individual parts.

a) MN:NK: The ratio MN:NK can be found by dividing the given ratio 6:8 into two parts. To do this, we need to divide 6 by the sum of the parts (6+8) and multiply the result by MN. Similarly, we divide 8 by the sum of the parts and multiply the result by NK.

MN:NK = (6 / (6+8)) * MN : (8 / (6+8)) * NK

Simplifying the expression, we get:

MN:NK = (6/14) * MN : (8/14) * NK

MN:NK = 3/7 * MN : 4/7 * NK

b) NK:MN: Similarly, the ratio NK:MN can be found by dividing the given ratio 6:8 into two parts. To do this, we need to divide 6 by the sum of the parts (6+8) and multiply the result by NK. Similarly, we divide 8 by the sum of the parts and multiply the result by MN.

NK:MN = (6 / (6+8)) * NK : (8 / (6+8)) * MN

Simplifying the expression, we get:

NK:MN = (6/14) * NK : (8/14) * MN

NK:MN = 3/7 * NK : 4/7 * MN

c) MK:MN: The ratio MK:MN can be found by dividing the given ratio 6:8 into two parts. To do this, we need to divide 6 by the sum of the parts (6+8) and multiply the result by MK. Similarly, we divide 8 by the sum of the parts and multiply the result by MN.

MK:MN = (6 / (6+8)) * MK : (8 / (6+8)) * MN

Simplifying the expression, we get:

MK:MN = (6/14) * MK : (8/14) * MN

MK:MN = 3/7 * MK : 4/7 * MN

Answer:

a) MN:NK = 3/7 * MN : 4/7 * NK b) NK:MN = 3/7 * NK : 4/7 * MN c) MK:MN = 3/7 * MK : 4/7 * MN