The area of a rectangle is 168 cm^2. The rectangle has a perimeter of 52 cm. What are the dimensions of the quadrilateral?

  12 cm by 14 cm

Step-by-step explanation:

The area is given by ...

  A = LW

The perimeter is given by ...

  P = 2(L +W)

Substituting the given values, we have ...

  168 = LW

  52 = 2(L +W)

The second equation can be used to find an expression for L:

  26 = L +W . . . . . divide by 2

  L = 26 -W . . . . . subtract W

Using this in the first equation, we have ...

  168 = (26 -W)(W)

  W² -26W +168 = 0

Factors of 168 are ...

  168 = (-1)(-168) = (-2)(-84) = (-3)(-56) = (-4)(-42) = (-6)(-28) = (-7)(-24)

     = (-8)(-21) = (-12)(-14)

Only the last factor pair (-12, -14) has a sum of -26, so the equation factors as ...

  (W -12)(W -14) = 0

Solutions are W=12, and W=14. The corresponding values of L are 14 and 12.

The quadrilateral has dimensions of 12 cm and 14 cm.

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)