Đáp án:
Áp dụng tính chất của dãy tỉ số bằng nhau:
a) Gọi độ dài 3 cạnh lần lượt là: a,b,c (a,b,c>0)
=> a:b:c= 3:4:5
Ta có: (a+b) - c= 4
$\begin{array}{l}
\dfrac{a}{3} = \dfrac{b}{4} = \dfrac{c}{5} = \dfrac{{a + b - c}}{{3 + 4 - 5}} = \dfrac{4}{2} = 2\\
\Rightarrow \left\{ \begin{array}{l}
a = 2.3 = 6\left( {cm} \right)\\
b = 2.4 = 8\left( {cm} \right)\\
c = 2.5 = 10\left( {cm} \right)
\end{array} \right.\\
\Rightarrow Chu\,vi:\\
C = a + b + c = 6 + 8 + 10 = 24\left( {cm} \right)\\
b)\dfrac{x}{3} = \dfrac{y}{7} = \dfrac{{x + y}}{{3 + 7}} = \dfrac{{ - 20}}{{10}} = - 2\\
\Rightarrow \left\{ \begin{array}{l}
x = - 2.3 = - 6\\
y = - 2.7 = - 14
\end{array} \right.\\
c) - 2.x = 3y\\
\Rightarrow \dfrac{x}{3} = \dfrac{y}{{ - 2}} = k\\
\Rightarrow \left\{ \begin{array}{l}
x = 3k\\
y = - 2k
\end{array} \right.\\
Do:x.y = - 54\\
\Rightarrow 3k.\left( { - 2k} \right) = - 54\\
\Rightarrow - 6.{k^2} = - 54\\
\Rightarrow {k^2} = 9\\
\Rightarrow \left[ \begin{array}{l}
k = 3\\
k = - 3
\end{array} \right.\\
+ Khi:k = 3 \Rightarrow \left\{ \begin{array}{l}
x = 9\\
y = - 6
\end{array} \right.\\
+ Khi:k = - 3 \Rightarrow \left\{ \begin{array}{l}
x = - 9\\
y = 6
\end{array} \right.\\
d)2x = 3y;5y = 7z\\
\Rightarrow \left\{ \begin{array}{l}
\dfrac{x}{3} = \dfrac{y}{2} \Rightarrow \dfrac{x}{{3.7}} = \dfrac{y}{{2.7}} = \dfrac{x}{{21}} = \dfrac{y}{{14}}\\
\dfrac{y}{7} = \dfrac{z}{5} \Rightarrow \dfrac{y}{{2.7}} = \dfrac{z}{{2.5}} = \dfrac{y}{{14}} = \dfrac{z}{{10}}
\end{array} \right.\\
\Rightarrow \dfrac{x}{{21}} = \dfrac{y}{{14}} = \dfrac{z}{{10}}\\
= \dfrac{{3x}}{{63}} = \dfrac{{7y}}{{98}} = \dfrac{{5z}}{{50}} = \dfrac{{3x - 7y + 5z}}{{63 - 98 + 50}} = \dfrac{{30}}{{15}} = 2\\
\Rightarrow \left\{ \begin{array}{l}
x = 42\\
y = 28\\
z = 20
\end{array} \right.
\end{array}$
