1-36. if the perimeter of the rectangle at right is 112 cm, which
equation below represents this fact? once you have selected the
appropriate equation, solve for x. homework
4x + 3
2x - 7
a. (2x - 7) +(4x + 3) = 112
b. 4(2x - 7) = 112
c. 2(2x - 7) + 2(4x + 3) = 112
d. (2x - 7)(4x + 3) = 112

2(2x - 7) + 2(4x + 3) = 112 ⇒ answer c

The value of x is 10

Step-by-step explanation:

* Lets explain how to solve the problem

- The perimeter of any rectangle is the sum of the lengths of its

  four sides

- Each two opposite sides in the rectangle are equal, then its

 perimeter is the sum of twice each dimensions

- P of the rectangle = 2L + 2W , where L and W are its dimensions

* Lets solve the problem

∵ The perimeter of the rectangle is 112 cm

∵ Its dimensions are (4x + 3) and (2x - 7)

∵ Perimeter of the rectangle = 2L + 2W

∴ 2(2x - 7) + 2(4x + 3) = 112

* We will chose the equation 2(2x - 7) + 2(4x + 3) = 112

* Lets solve the equation

∵ 2(2x - 7) + 2(4x + 3) = 112

- Multiply each bracket by the number in front of it

∵ 2(2x - 7) = 2(2x) - 2(7) = 4x - 14

∵ 2(4x + 3) = 2(4x) + 2(3) = 8x + 6

∴ 4x - 14 + 8x + 6 = 112

- Collect the like terms

∵ (4x + 8x) + (-14 + 6) = 12x - 8

∴ 12x - 8 = 112

- Add 8 for both sides

∴ 12x = 120

- Divide both sides by 12

∴ x = 10

* The value of x is 10