Rectangle 7768

The base of a cuboid is a rectangle. The ratio of its length to width is 3:2. The length of the rectangle of the base is in the ratio of 4:5 to the height of the block. The sum of the lengths of all the edges of the block is 2.8m. Find:
a) the surface of the cuboid in cm²
b) volume in dm³

Correct answer:

S =  50688 cm²
V =  737280 cm³

Step-by-step explanation:

$$\begin{gathered} a=3/2\cdot b \\ a=4/5\cdot c \\ a+b+c=2.8\cdot 100 \\ 2a-3b=0 \\ 5a-4c=0 \\ a+b+c=280 \\ Pivot:Row1\leftrightarrow Row2 \\ 5a-4c=0 \\ 2a-3b=0 \\ a+b+c=280 \\ Row2-\frac{2}{5}\cdot Row1\to Row2 \\ 5a-4c=0 \\ -3b+1.6c=0 \\ a+b+c=280 \\ Row3-\frac{1}{5}\cdot Row1\to Row3 \\ 5a-4c=0 \\ -3b+1.6c=0 \\ b+1.8c=280 \\ Row3-\frac{1}{-3}\cdot Row2\to Row3 \\ 5a-4c=0 \\ -3b+1.6c=0 \\ 2.333c=280 \\ c=\frac{280}{2.33333333}=120 \\ b=\frac{0-1.6c}{-3}=\frac{0-1.6\cdot 120}{-3}=64 \\ a=\frac{0+4c}{5}=\frac{0+4\cdot 120}{5}=96 \\ a=96 \\ b=64 \\ c=120 \\ S=2\cdot (a\cdot b+b\cdot c+c\cdot a)=2\cdot (96\cdot 64+64\cdot 120+120\cdot 96)=50688{\text{cm}}^2 \end{gathered}$$

$V=a\cdot b\cdot c=96\cdot 64\cdot 120=737280{\text{cm}}^3$

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