Answer:
x = 1.52
Explanation:
I don't know if there is a specific way to solve this problem, but I will just do it the complicated way, sorry haha...
Follow these steps.
1. Create a formula to solve the problem
- The question is basically saying when is the area of the rectangle equal to the area of the circle?
- To make a formula for this, let's identify the equation for the Area for both figures and THEN set them equal to each other.
Area of a Rectangle = Length x Width
Area of a Circle = πr²
Setting them equal to each other ⇒ Length x Width = πr²
This will be the formula we use ..
2. Plug in all the information
Length = 4x - 2
Width = x + 8
r (radius of the circle) = x + 2
Put all these small expressions in the equation we made.
Final equation: (4x - 2) × (x + 8) = π( x + 2)²
3. Now solve!
4X² + 32x - 2x - 16 = π × (x² + 4x + 4)
Keep solving! (But to make things easier, let's just use 3.14 instead of the whole number for pi)
4x² + 30x - 16 = 3.14( x² + 4x + 4)
4x² + 30x - 16 = 3.14x² + 12.56x + 12.56
Combine like terms
0.86x² + 17.44x - 28.56 = 0
4. Trial and Error
- I'm going to plug in all the answers in our magic equation to see what fits. (I won't show this because it's messy)
Final answer: x = 1.52
Yikes! That problem was so messy, but we did it! Let me know if you have questions about my process and I'll explain further.
:)