Question

given:

• twnb ≅ rdhy
• nw = 4x,
• rd = 5x - 27,
• ry = 2x + 6,
• hd = 6x - 25,
• tw = 3x - 2,
• bn = x + 9

find the values below.
x = units
rd = units
submit
mistakes: 0/5

Explanation:

Step1: Use the property of congruent polygons

Since \(TWNB\cong RDHY\), their corresponding sides are equal. \(NW = RD\) (corresponding sides of congruent polygons).
Given \(NW = 4x\) and \(RD=5x - 27\), we set up the equation \(4x=5x - 27\).

Step2: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(4x-4x=5x - 27-4x\).
We get \(0=x - 27\).
Add \(27\) to both sides: \(x=27\).

Step3: Find the value of \(RD\)

Substitute \(x = 27\) into the formula for \(RD\).
\(RD=5x - 27\), so \(RD=5\times27-27\).
Using the distributive property \(a\times c - b\times c=(a - b)\times c\), here \(a = 5\), \(b = 1\), \(c = 27\).
\(RD=(5 - 1)\times27=4\times27 = 108\).

Answer:

\(x = 27\) units, \(RD=108\) units