The answer for the question shown above is the las option, which is: <span>D. 2:3 and 4:9.
The explanation is shown below:
1. You have that</span><span> widths of the two similar rectangles are 10 cm and 15 cm. Therefore:
</span> ratio=10:15
ratio=2:3
2- So, the ratio of the perimeter is:
ratio of the perimeter= 2:3
3- The ratio of the areas is:
ratio of the areas=2²:3²
ratio of the areas=4:9
Answer:
B) ![\frac{\sqrt{3} + \sqrt{6} }{8}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%20%2B%20%5Csqrt%7B6%7D%20%7D%7B8%7D)
Step-by-step explanation:
The given expression is ![\frac{(3 + \sqrt{18} }{4\sqrt{12} }](https://tex.z-dn.net/?f=%5Cfrac%7B%283%20%2B%20%5Csqrt%7B18%7D%20%7D%7B4%5Csqrt%7B12%7D%20%7D)
We should not have the radical sign in the denominator. To get rid of the radical number, we multiply both the numerator and the denominator by 4√12.
= ![\frac{(3 + \sqrt{18} }{4\sqrt{12} } * \frac{4\sqrt{12} }{4\sqrt{12} }](https://tex.z-dn.net/?f=%5Cfrac%7B%283%20%2B%20%5Csqrt%7B18%7D%20%7D%7B4%5Csqrt%7B12%7D%20%7D%20%2A%20%5Cfrac%7B4%5Csqrt%7B12%7D%20%7D%7B4%5Csqrt%7B12%7D%20%7D)
= ![\frac{12\sqrt{12} + 4\sqrt{18} \sqrt{12} }{16*12}](https://tex.z-dn.net/?f=%5Cfrac%7B12%5Csqrt%7B12%7D%20%2B%204%5Csqrt%7B18%7D%20%5Csqrt%7B12%7D%20%20%7D%7B16%2A12%7D)
= ![\frac{24\sqrt{3} + 24\sqrt{6} }{192}](https://tex.z-dn.net/?f=%5Cfrac%7B24%5Csqrt%7B3%7D%20%2B%2024%5Csqrt%7B6%7D%20%20%20%7D%7B192%7D)
= ![\frac{24(\sqrt{3}+\sqrt{6} ) }{192} \\](https://tex.z-dn.net/?f=%5Cfrac%7B24%28%5Csqrt%7B3%7D%2B%5Csqrt%7B6%7D%20%29%20%7D%7B192%7D%20%5C%5C)
Now we can cancel out 24/192, which is 1/8
= ![\frac{\sqrt{3}+\sqrt{6} }{8}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7B3%7D%2B%5Csqrt%7B6%7D%20%20%7D%7B8%7D)
Answer is B.
Thank you.
28/50 * 100 = 56%
when finding percentage always multiply by 200
Answer:
273 tiles
Step-by-step explanation:
Given
Square tile
![Side=\frac{1}{2} ft](https://tex.z-dn.net/?f=Side%3D%5Cfrac%7B1%7D%7B2%7D%20ft)
Bathroom floor
![Length = 10\frac{1}{2}ft](https://tex.z-dn.net/?f=Length%20%3D%2010%5Cfrac%7B1%7D%7B2%7Dft)
![Width = 6\frac{1}{2}ft](https://tex.z-dn.net/?f=Width%20%3D%206%5Cfrac%7B1%7D%7B2%7Dft)
Required
Determine the number of tiles to cover the floor
First, we calculate the area of the floor:
![A_{floor} = Length * Width](https://tex.z-dn.net/?f=A_%7Bfloor%7D%20%3D%20Length%20%2A%20Width)
![A_{floor} = 10\frac{1}{2} * 6\frac{1}{2}](https://tex.z-dn.net/?f=A_%7Bfloor%7D%20%3D%2010%5Cfrac%7B1%7D%7B2%7D%20%2A%206%5Cfrac%7B1%7D%7B2%7D)
Convert to decimals
![A_{floor} = 10.5 * 6.5](https://tex.z-dn.net/?f=A_%7Bfloor%7D%20%3D%2010.5%20%2A%206.5)
![A_{floor} = 68.25ft^2](https://tex.z-dn.net/?f=A_%7Bfloor%7D%20%3D%2068.25ft%5E2)
Next, we calculate the area of the square tile:
![A_{tile} = Side * Side](https://tex.z-dn.net/?f=A_%7Btile%7D%20%3D%20Side%20%2A%20Side)
![A_{tile} = \frac{1}{2} * \frac{1}{2}](https://tex.z-dn.net/?f=A_%7Btile%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A%20%5Cfrac%7B1%7D%7B2%7D)
Convert to decimal
![A_{tile} = 0.5 * 0.5](https://tex.z-dn.net/?f=A_%7Btile%7D%20%3D%200.5%20%2A%200.5)
![A_{tile} = 0.25ft^2](https://tex.z-dn.net/?f=A_%7Btile%7D%20%3D%200.25ft%5E2)
The number of tiles is then calculated as:
![Tiles = \frac{A_{floor}}{A_{tile}}](https://tex.z-dn.net/?f=Tiles%20%3D%20%5Cfrac%7BA_%7Bfloor%7D%7D%7BA_%7Btile%7D%7D)
![Tiles = \frac{68.25ft^2}{0.25ft^2}](https://tex.z-dn.net/?f=Tiles%20%3D%20%5Cfrac%7B68.25ft%5E2%7D%7B0.25ft%5E2%7D)
![Tiles = \frac{68.25}{0.25}](https://tex.z-dn.net/?f=Tiles%20%3D%20%5Cfrac%7B68.25%7D%7B0.25%7D)
![Tiles = 273](https://tex.z-dn.net/?f=Tiles%20%3D%20273)
FALSE!
Equation only gives us the information about Extreme Points of that line.
Hope this helps!