A quarter of the length of the MN segment is equal to half the length of the segment KP

A quarter of the length of the MN segment is equal to half the length of the segment KP, which is 24 cm shorter. Find the length of each line.

1. By the condition of the problem, it is known that a quarter of the segment МN is half the length of the segment КР, which is 24 cm shorter.

Let us denote the length of MN as x cm, and KP as y cm.

2. Let’s compose two equations:

a) x = y + 24;

b) 1/4 x = 1/2 y;

Let’s solve the system using the substitution method:

the value of y in b) is expressed in terms of x from a) and we get:

(y + 24): 4 = y: 2; we bring to a common denominator and then y + 24 = 2 y, that is, y = 24 cm.

Let’s calculate what is the length of the segment MN = 24 + 24 = 48 cm.

Answer: The segment MN is 48 cm, and the KR is 24 cm.