Answer:
6 in
Step-by-step explanation:
Let x = the side length of the original square.
They removed 3 in from each side of the original square, so the side lengths of the remaining square are x - 3 in.
The area of the smaller square is (x - 3)².
The area of the original square is x²
I assume the area of the smaller square is ¼ that of the original square. Then
1. Solve for x
![\begin{array}{rcl}\frac{1}{4}x^{2} & = & (x - 3)^{2}\\x^{2} & = & 4(x - 3)^{2}\\& = & 4(x^{2} - 6x + 9)\\x^{2}& = & 4x^{2} - 24x + 36\\3x^{2} - 24x + 36 & = & 0\\x^{2} - 8x + 12 & = & 0\\(x - 2)(x - 6) & = & 0\\x - 2 = 0& \qquad &x - 6 = 0\\x = 2& \qquad &x = 6\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D%5Cfrac%7B1%7D%7B4%7Dx%5E%7B2%7D%20%26%20%3D%20%26%20%28x%20-%203%29%5E%7B2%7D%5C%5Cx%5E%7B2%7D%20%26%20%3D%20%26%204%28x%20-%203%29%5E%7B2%7D%5C%5C%26%20%3D%20%26%204%28x%5E%7B2%7D%20-%206x%20%2B%209%29%5C%5Cx%5E%7B2%7D%26%20%3D%20%26%204x%5E%7B2%7D%20-%2024x%20%2B%2036%5C%5C3x%5E%7B2%7D%20-%2024x%20%2B%2036%20%26%20%3D%20%26%200%5C%5Cx%5E%7B2%7D%20-%208x%20%2B%2012%20%26%20%3D%20%26%200%5C%5C%28x%20-%202%29%28x%20-%206%29%20%26%20%3D%20%26%200%5C%5Cx%20-%202%20%3D%200%26%20%5Cqquad%20%26x%20-%206%20%3D%200%5C%5Cx%20%3D%202%26%20%5Cqquad%20%26x%20%3D%206%5C%5C%5Cend%7Barray%7D)
2. Calculate the side length of the smaller square
(a) x = 2
Side length = x - 3 = 2 - 3 = -1 in.
IMPOSSIBLE. You can't have a negative side length.
(b) x = 6
Side length of smaller square = 6 - 3 = 3 in.
Side length of original square = x = 6 in
Check:
![\begin{array}{rcl}\frac{1}{4}(6)^{2} & = & (6 - 3)^{2}\\\frac{1}{4}\times 36 & = & 3^{2}\\9 & = & 9\\\end{array}](https://tex.z-dn.net/?f=%5Cbegin%7Barray%7D%7Brcl%7D%5Cfrac%7B1%7D%7B4%7D%286%29%5E%7B2%7D%20%26%20%3D%20%26%20%286%20-%203%29%5E%7B2%7D%5C%5C%5Cfrac%7B1%7D%7B4%7D%5Ctimes%2036%20%26%20%3D%20%26%203%5E%7B2%7D%5C%5C9%20%26%20%3D%20%26%209%5C%5C%5Cend%7Barray%7D)
OK.
Answer:
91/4 simplified = 22 3/4
work:
subtract find answer then simplify :)
Hope this helps
Answer:
x = 2
Step-by-step explanation:
Set the equations equal to each other
x + 2 = -3x + 10
+ 3x + 3x Add 3x to both sides
4x + 2 = 10
- 2 - 2 Subtract 2 from both sides
4x = 8 Divide both sides by 4
x = 2
If this answer is correct, please make me Brainliest!