Question

The points H, I, J and K all lie on the same line segment, in that order, such that the

ratio of HI: IJ: JK is equal to 2:1: 2. If HK = 25, find JK.

Answer 1

The length of the segment JK is found using the ratio given for the segments HI, IJ, and JK. By assigning a value to the single ratio unit and solving for it, we calculated that the length of JK is 10 units.

Step-by-step explanation:

If the points H, I, J, and K all lie on the same line segment in that order, and the ratio of HI: IJ: JK is 2:1:2, and HK equals 25, we need to find the length of JK. To solve this, we consider the given ratio as parts of the whole segment. Let's assign a variable 'x' to represent one part, then HI and JK both would be 2x and IJ would be x. Since HK is the whole segment, we can write the equation 2x + x + 2x = 25. Solving for 'x', we get 5x = 25 and therefore, x = 5. Now, we can find JK by multiplying x by 2. Therefore, JK = 2x = 2(5) = 10.

Answer 2

Step-by-step explanation:

Given,

ratio of HI, IJ , Jk = 2 : 1 : 2

let their value be

HI = 2x

IJ = x

JK = 2x

HK = 25

according to question,

HI + IJ + JK = Hk

now, after inserting the values we got,

→ 2x + x + 2x = 25

→ 5x = 25

→ x = 25/5 = 5

→ x = 5

therefore value of,

HI = 2x → 2×5 = 10

IJ = x → 5

JK = 2x → 2×5 = 10

Hence, value of JK is 10.

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