Question

what values of b and c make δrst ≅ δzyx?
triangle rst with right angle at r, side st labeled 5b, side sr labeled 12c.
triangle zyx with right angle at z, side yx labeled 4c+24, side zx labeled 4b+17.
find b =
find c =

Explanation:

Step1: Solve for \( b \)

Since \( \triangle RST \cong \triangle ZYX \), their corresponding sides are equal. The side \( ST = 5b \) and \( XY = 4b + 17 \). So we set up the equation:
\( 5b = 4b + 17 \)
Subtract \( 4b \) from both sides:
\( 5b - 4b = 4b + 17 - 4b \)
\( b = 17 \)

Step2: Solve for \( c \)

The side \( RS = 12c \) and \( YZ = 4c + 24 \). Since the triangles are congruent, these sides are equal:
\( 12c = 4c + 24 \)
Subtract \( 4c \) from both sides:
\( 12c - 4c = 4c + 24 - 4c \)
\( 8c = 24 \)
Divide both sides by 8:
\( c = \frac{24}{8} = 3 \)

Answer:

\( b = 17 \), \( c = 3 \)