Question

Please help me solve for x =

Answer 1

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:

$\frac{ML}{NM} = \frac{ST}{PS}$

$\frac{8}{10} = \frac{x - 1}{x + 2}$

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:

$\frac{26}{2} = \frac{2x}{2}$

13 = x

Verify whether x = 13 is the correct value:

$\frac{ML}{NM} = \frac{ST}{PS}$

$\frac{8}{10} = \frac{x - 1}{x + 2}$

$\frac{8/2}{10/2} = \frac{4}{5}$

$\frac{x -1}{x+2} = \frac{13 - 1}{13 + 2} = \frac{12}{15} = \frac{12 / 3}{15 /3} = \frac{4}{5}$

This shows the proportional relationship between $\frac{ML}{NM} = \frac{ST}{PS}$, and that ΔNML and ΔPST are indeed similar right triangles.

Therefore, the correct answer is x = 13.