Question

if jklm is a parallelogram, find its perimeter.
k 3y - 4 l
6x - 14 x + 11
j 5y - 22 m
the perimeter of this parallelogram is the sum of all sides.

Explanation:

Step1: Use properties of parallelogram (opposite sides equal) to find x.

In a parallelogram, \( JK = LM \) and \( KL = JM \). So, \( 6x - 14 = x + 11 \).
Subtract \( x \) from both sides: \( 5x - 14 = 11 \).
Add 14 to both sides: \( 5x = 25 \).
Divide by 5: \( x = 5 \).

Step2: Find length of sides with x.

Substitute \( x = 5 \) into \( 6x - 14 \): \( 6(5) - 14 = 30 - 14 = 16 \).
Substitute \( x = 5 \) into \( x + 11 \): \( 5 + 11 = 16 \) (consistent, as expected).

Step3: Use properties of parallelogram to find y.

Since \( KL = JM \), \( 3y - 4 = 5y - 22 \).
Subtract \( 3y \) from both sides: \( -4 = 2y - 22 \).
Add 22 to both sides: \( 18 = 2y \).
Divide by 2: \( y = 9 \).

Step4: Find length of sides with y.

Substitute \( y = 9 \) into \( 3y - 4 \): \( 3(9) - 4 = 27 - 4 = 23 \).
Substitute \( y = 9 \) into \( 5y - 22 \): \( 5(9) - 22 = 45 - 22 = 23 \) (consistent).

Step5: Calculate perimeter.

Perimeter of parallelogram is \( 2\times(16 + 23) \) (since opposite sides are equal, sum of two adjacent sides times 2).
\( 2\times(39) = 78 \).

Answer:

78