Question

Explain how to find the value of y that would make segment OP parallel to segment LN.

Answer 1

y= 36

Explanation:

also ily, no homo

Answer 2

`y = 36`

Explanation:

Given; the triangle above

Required

Find y

This question falls under the topic/subtopic similar triangles where we need to make comparison between similar sides'

But first, it should be noted that triangle MOP is similar to triangle MLN

This implies that

Side MP is similar to MN

Side MO is similar to ML

Mathematically; This can be represented as follows;

`(MP)/(MN) = (MO)/(ML)`

Where MP =y; MN = y + 18; MO = 28; ML = 28 + 14

Substitute these values in the above expression

`(y)/(y+18) = (28)/(28+14)`

`(y)/(y+18) = (28)/(42)`

Multiply both sides by 42

`42 * (y)/(y+18) = (28)/(42) * 42`

`(42y)/(y+18) = (28*42)/(42)`

`(42y)/(y+18) = 28`

Multiply both sides by y + 18

`(y+18)*(42y)/(y+18) = 28 * (y+18)`

`42y = 28 * (y+18)`

Open Bracket

`42y = 28 * y+28 * 18`

`42y = 28y+504`

Subtract 28y from both sides

`42y - 28y = 28y - 28y +504`

`14y = 504`

Divide both sides by 14

`(14y)/(14) = (504)/(14)`

`y = (504)/(14)`

`y = 36`