Answer:
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
