Answer:
x = 13
Step-by-step explanation:
Given that Δ NML and Δ PST are similar right triangles, we can set up the following proportional statement to establish their relationship:
[tex]\frac{ML}{NM} = \frac{ST}{PS}[/tex]
[tex]\frac{8}{10} = \frac{x - 1}{x + 2}[/tex]
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:
[tex]\frac{26}{2} = \frac{2x}{2}[/tex]
13 = x
Verify whether x = 13 is the correct value:
[tex]\frac{ML}{NM} = \frac{ST}{PS}[/tex]
[tex]\frac{8}{10} = \frac{x - 1}{x + 2}[/tex]
[tex]\frac{8/2}{10/2} = \frac{4}{5}[/tex]
[tex]\frac{x -1}{x+2} = \frac{13 - 1}{13 + 2} = \frac{12}{15} = \frac{12 / 3}{15 /3} = \frac{4}{5}[/tex]
This shows the proportional relationship between [tex]\frac{ML}{NM} = \frac{ST}{PS}[/tex], and that ΔNML and ΔPST are indeed similar right triangles.
Therefore, the correct answer is x = 13.
