Question

Please help me solve for x =

I message my teacher she said the side are not equal to each other, they are proportional ( please help me awnser)

Answer 1

x = 13

Explanation:

Given that Δ NML and Δ PST are similar right triangles, we can set up the following proportional statement to establish their relationship:

`(ML)/(NM) = (ST)/(PS)`

`(8)/(10) = (x - 1)/(x + 2)`

Cross multiply:

8(x + 2) = 10 (x - 1)

8x + 16 = 10x - 10

Subtract 8x from both sides:

8x - 8x + 16 = 10x - 8x - 10

16 = 2x - 10

Add 10 to both sides:

16 + 10 = 2x - 10 + 10

26 = 2x

Divide both sides by 2:

`(26)/(2) = (2x)/(2)`

13 = x

Verify whether x = 13 is the correct value:

`(ML)/(NM) = (ST)/(PS)`

`(8)/(10) = (x - 1)/(x + 2)`

`(8/2)/(10/2) = (4)/(5)`

`(x -1)/(x+2) = (13 - 1)/(13 + 2) = (12)/(15) = (12 / 3)/(15 /3) = (4)/(5)`

This shows the proportional relationship between
`(ML)/(NM) = (ST)/(PS)`, and that ΔNML and ΔPST are indeed similar right triangles.

Therefore, the correct answer is x = 13.