Question

which of the following statements are true? select all that apply.
a) the perimeter of quadrilateral 1 is 13x + 6.
b) the perimeter of quadrilateral 1 is 11x + 9.
c) the perimeter of quadrilateral 2 is 14x - 5.
d) the perimeter of quadrilateral 2 is 11x + 1.
e) if x = 3, quadrilateral 1 has the greater perimeter.
f) if x = 4, quadrilateral 1 has the greater perimeter.

Explanation:

Step1: Calculate perimeter of Quadrilateral 1

The perimeter \(P_1\) of Quadrilateral 1 is the sum of its sides.
\(P_1=2(2x - 3)+5x+6 + 4x+6\)

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Step2: Calculate perimeter of Quadrilateral 2

The perimeter \(P_2\) of Quadrilateral 2 is the sum of its sides.
\(P_2=(2x + 4)+12+3(3x - 7)+3x\)

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Step3: Check option A

Since \(P_1 = 13x+6\), option A is correct.

Step4: Check option B

Since \(P_1
eq11x + 9\), option B is incorrect.

Step5: Check option C

Since \(P_2=14x-5\), option C is correct.

Step6: Check option D

Since \(P_2
eq11x + 1\), option D is incorrect.

Step7: When \(x = 3\)

\(P_1=13\times3+6=39 + 6=45\), \(P_2=14\times3-5=42-5 = 37\). So \(P_1>P_2\), option E is correct.

Step8: When \(x = 4\)

\(P_1=13\times4+6=52+6 = 58\), \(P_2=14\times4-5=56-5 = 51\). So \(P_1>P_2\), option F is correct.

Answer:

A. The perimeter of Quadrilateral 1 is \(13x + 6\), C. The perimeter of Quadrilateral 2 is \(14x-5\), E. If \(x = 3\), Quadrilateral 1 has the greater perimeter, F. If \(x = 4\), Quadrilateral 1 has the greater perimeter.