The MK segment is 2 times longer than the AB segment, the SD segment is 3 times shorter than the AB segment.

| April 3, 2021 | education

The MK segment is 2 times longer than the AB segment, the SD segment is 3 times shorter than the AB segment. What is the length of each segment if it is known that the length of 3 segments is 100 cm.

Let the length of the segment SD be x cm, then the length of the segment AB is 3x cm (if SD is 3 times shorter than AB, then the segment AB, on the contrary, is 3 times longer than the segment SD), and the length of the segment MK is (2 * 3x) cm. it is known to the condition of the problem that the length of the three segments together is equal to (x + 3x + 2 * 3x) cm or 100 cm. Let’s compose an equation and solve it.

x + 3x + 2 * 3x = 100;

x + 3x + 6x = 100;

10x = 100;

x = 100: 10;

x = 10 (cm) – SD;

3x = 10 * 3 = 30 (cm) – AB;

2 * 3x = 30 * 2 = 60 (cm) – MK.

Answer. AB = 30 cm, MK = 60 cm, SD = 10 cm.



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