Question

find the value of the variable y = options: altitude, base, hypotenuse, median (triangle diagram with sides y, y - 1, 18, 16)

Explanation:

Step1: Set up proportion for similar triangles

Since the triangles are similar, the ratios of corresponding sides are equal:
$\frac{y}{18} = \frac{y-1}{16}$

Step2: Cross-multiply to eliminate fractions

$16y = 18(y-1)$

Step3: Expand the right-hand side

$16y = 18y - 18$

Step4: Rearrange to solve for $y$

$18 = 18y - 16y$
$18 = 2y$
$y = \frac{18}{2}$

Answer:

$y = 9$