Point K divides segment AB in a ratio of 5: 7. How many centimeters is the length of the AB

Point K divides segment AB in a ratio of 5: 7. How many centimeters is the length of the AB segment if it is 40 cm larger than the KB segment ..

We know that point K divides the segment AB in the ratio of 5: 7, that is, AB = AK + KB. And if AB is an integer value, that is, 1, then we can represent the segments as fractions:

AB = 1 = (5 + 7) / (5 + 7) = 12/12.

AK = 5/12.

CВ = 7/12.

From the conditions we know that AB is more than the length of the KB segment by 40 cm, that is, AB = KB + 40 (cm).

If AB = AK + KB, then AK = 40 (cm).

Let’s make a proportion using the fractions we compiled:

5/12 – 40 (cm)

12/12 – AB (cm).

AB = (12/12 * 40) / 5/12 = (1 * 40) / 5/12 = 40/5/12 = 96 cm.

a) 96 cm; b) 68 cm; c) 102 cm; d) 124.

Answer: the correct answer is 96 cm.