Answer:
CD=14 cm and DE=21 cm
Step-by-step explanation:
Let the rhombus's side be x cm, DN=NF=FM=DM=x xm.
Triangles CDE and FNE are similar, thus,
![\dfrac{CD}{FN}=\dfrac{CE}{FE}=\dfrac{DE}{NE}](https://tex.z-dn.net/?f=%5Cdfrac%7BCD%7D%7BFN%7D%3D%5Cdfrac%7BCE%7D%7BFE%7D%3D%5Cdfrac%7BDE%7D%7BNE%7D)
or
![\dfrac{CD}{x}=\dfrac{8+12}{12}=\dfrac{DE}{DE-x}.](https://tex.z-dn.net/?f=%5Cdfrac%7BCD%7D%7Bx%7D%3D%5Cdfrac%7B8%2B12%7D%7B12%7D%3D%5Cdfrac%7BDE%7D%7BDE-x%7D.)
Hence,
![CD=\dfrac{5x}{3}](https://tex.z-dn.net/?f=CD%3D%5Cdfrac%7B5x%7D%7B3%7D)
and
![20(DE-x)=12DE,\\ \\8DE=20x,\\ \\DE=\dfrac{5x}{2}.](https://tex.z-dn.net/?f=20%28DE-x%29%3D12DE%2C%5C%5C%20%5C%5C8DE%3D20x%2C%5C%5C%20%5C%5CDE%3D%5Cdfrac%7B5x%7D%7B2%7D.)
Since the perimeter of the triangle CDE is 55 cm, we have that
![\dfrac{5x}{3}+\dfrac{5x}{2}+20=55,\\ \\\dfrac{25x}{6}=35,\\ \\x=\dfrac{6\cdot 35}{25}=8.4.](https://tex.z-dn.net/?f=%5Cdfrac%7B5x%7D%7B3%7D%2B%5Cdfrac%7B5x%7D%7B2%7D%2B20%3D55%2C%5C%5C%20%5C%5C%5Cdfrac%7B25x%7D%7B6%7D%3D35%2C%5C%5C%20%5C%5Cx%3D%5Cdfrac%7B6%5Ccdot%2035%7D%7B25%7D%3D8.4.)
Therefore, CD=14 cm and DE=21 cm
Answer:
The paint will not fill the tray by 10.53 in3.
Step-by-step explanation:
Length = 14 inches
Width = 10 inches
Depth = 4 cm = 1.57 inches
Volume = length x width x depth
Volume = 14 x 10 x 1.57
= 220.47 inches cube
Volume of Gallon = 231 inches cube
(3x -20) / 56 = 9/72
72(3x - 20) = 9 (56)
216x - 1440 = 504
216x = 1944
x = 9
This is the correct answer is X=0 and y= 4.