Point K belongs to segment AB, the length of which is 15 cm. What are the lengths of segments AK and BK if: segment AK

Point K belongs to segment AB, the length of which is 15 cm. What are the lengths of segments AK and BK if: segment AK is 6 cm less than segment BK; segment AK is twice as large as segment BK?

1) Consider the first condition when the segment AK is 6 cm less than the segment BK.

Let us denote the segment AK by – x;

Then the segment BK = AK + 6.

Let’s make the equation:

AK + BK = AB, replace with the corresponding values:

x + x +6 = 15, then we solve the equation;

2x = 15 – 6

2x = 11

x = 5.5 cm – the length of the AK segment.

Let’s find the length of the segment BK:

15 – 5.5 = 9.5 CM

Answer: AK = 5.5 CM, BK = 9.5 CM.

2) Consider the condition when the segment AK is twice as large as the segment BK.

Let us denote the segment BK by – x;

Then the segment AK = 2 * x.

Let’s make the equation:

AK + BK = AB

2 * x + x = 15

3 x = 15

x = 15/3

x = 5 cm

Segment BK = 5 cm.

Let’s find the segment AK:

AK = AB – VK

15 – 5 = 10 cm

Segment AK = 10 CM.

Answer: AK = 10 CM, BK = 5 cm.