Triangle sides

If we increase one side of the triangle by 11 cm and reduce the other by 11 cm, we get an equilateral triangle. Four times the shortest side of the triangle is 10 cm greater than three times the triangle's longest side. Find all the lengths of the sides of the triangle.

Final Answer:

x =  76 cm
y =  98 cm
z =  87 cm

Step-by-step explanation:

$$\begin{gathered} x+11=y-11 \\ 4x=10+3y \\ 4\cdot x=10+3\cdot y \\ x-y=-22 \\ 4x-3y=10 \\ Pivot:Row1\leftrightarrow Row2 \\ Row2-\frac{1}{4}\cdot Row1\to Row2 \\ -0.25y=-24.5 \\ y=\frac{-24.5}{-0.25}=98 \\ x=\frac{10+3y}{4}=\frac{10+3\cdot 98}{4}=76=76\text{cm} \\ x=76 \\ y=98 \end{gathered}$$

$z=x+11=76+11=87\text{cm}$

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