Given that a quadrilateral PQRS is a parallelogram, PQ and RS are opposite sides, PQ = 7x + 16, RS = 5x +28, and QR = 67 which of the following statements are correct? More than one answer may be correct.

PQ = 58

Perimeter = 250

Opposite sides are congruent

Step-by-step explanation:

PQ = 58:

Because PQRS is a parallelogram, PQ equals RS.

1. Set up the equation and solve

7x + 16 = 5x + 28

2x = 12

x = 6

2. Plug in x into PQ

7(6) + 16 = 58

Perimeter = 250:

PQ = RS and QR = SP

1. Add the sides

58 + 58 + 67 + 67 = 250

Opposite sides are congruent:

definition of a parallelogram

this doesn't make sense lol

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)