On the beam AM, the segments AB and AC were laid, AC = 89 cm. Find the length of the segment

| September 1, 2021 | education

On the beam AM, the segments AB and AC were laid, AC = 89 cm. Find the length of the segment BC if: a) AB is 15 cm longer than AC; b) AB is 15 cm shorter than AC.

a) Let the length of the segment BC = x cm.Since on the ray AM we laid the segments AB and AC so that AB is 15 cm longer than AC, that is, AB = 15 + AC, then point C lies between points A and B, which means that AB = AC + BC or 15 + AC = AC + BC. Knowing that AC = 89 cm, we make the equation:

15 + 89 = 89 + x;

x = 15 (cm) – the length of the segment BC.

Answer: the length of the segment BC is 15 cm.

b) Let the length of the segment BC = x cm.Since on the beam AM we laid the segments AB and AC so that AB is 15 cm shorter than AC, that is, AB = AC – 15, then point B lies between points A and C, which means that AC = AB + BC or AC = (AC – 15) + BC. Knowing that AC = 89 cm, we make the equation:

89 = (89 – 15) + x;

x = 15 (cm) – the length of the segment BC.

Answer: the length of the segment BC is 15 cm.



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