Question

if a ⊥ c, c || b, xs = 10, and xy = 24 what is ry?
a. 10
b. 26
c. 24
d. 28

Explanation:

Step1: Identify Triangle Type

Since \( a \perp c \) and \( c \parallel b \), \( a \perp b \). So \( \triangle RXY \) and \( \triangle SXY \) are right triangles, and \( RX = XS = 10 \) (given segments on \( b \) are equal). \( XY = 24 \) (leg of right triangle).

Step2: Apply Pythagorean Theorem

For right triangle \( RXY \), \( RY = \sqrt{RX^2 + XY^2} \). Substitute \( RX = 10 \), \( XY = 24 \):
\( RY = \sqrt{10^2 + 24^2} = \sqrt{100 + 576} = \sqrt{676} = 26 \).

Answer:

B. 26