Đề thi khảo sát chất lượng đầu năm - Đề số 2

Chiều rộng của cái sân là: $\dfrac{{77}}{5}:\dfrac{{22}}{5} = \dfrac{{77}}{5}.\dfrac{5}{{22}} = \dfrac{7}{2}\,\left( m \right)$

Chu vi của cái sân là: $2.\left( {\dfrac{{22}}{5} + \dfrac{7}{2}} \right) = \dfrac{{79}}{5}\,\left( m \right).$

$\begin{array}{l}13\dfrac{3}{x} = \dfrac{{136}}{{10}}\\ \Rightarrow \dfrac{{13x + 3}}{x} = \dfrac{{136}}{{10}}\\ \Rightarrow 10.\left( {13x + 3} \right) = 136x\\ \Rightarrow 10.13x + 10.3 = 136x\\ \Rightarrow 130x + 30 = 136x\\ \Rightarrow 130x - 136x =  - 30\\ \Rightarrow x.\left( {130 - 136} \right) =  - 30\\ \Rightarrow \left( { - 6} \right).x =  - 30\\ \Rightarrow x = \left( { - 30} \right):\left( { - 6} \right)\\ \Rightarrow x = 5\end{array}$

$A = \dfrac{{34}}{{7.13}} + \dfrac{{51}}{{13.22}} + \dfrac{{85}}{{22.37}} + \dfrac{{68}}{{37.49}}$

$= \dfrac{{34}}{6}.\dfrac{6}{{7.13}} + \dfrac{{51}}{9}.\dfrac{9}{{13.22}}$$\, + \dfrac{{85}}{{15}}.\dfrac{1}{{22.37}} + \dfrac{{68}}{{12}}.\dfrac{{12}}{{37.49}}$

$= \dfrac{{17}}{3}.\left( {\dfrac{1}{7} - \dfrac{1}{{13}}} \right) + \dfrac{{17}}{3}.\left( {\dfrac{1}{{13}} - \dfrac{1}{{22}}} \right)$$\,+ \dfrac{{17}}{3}.\left( {\dfrac{1}{{22}} - \dfrac{1}{{37}}} \right)$$\,+ \dfrac{{17}}{3}.\left( {\dfrac{1}{{37}} - \dfrac{1}{{49}}} \right)$

$= \dfrac{{17}}{3}.\dfrac{1}{7} - \dfrac{{17}}{3}.\dfrac{1}{{13}} + \dfrac{{17}}{3}.\dfrac{1}{{13}}$$\,- \dfrac{{17}}{3}.\dfrac{1}{{22}} + \dfrac{{17}}{3}.\dfrac{1}{{22}} - \dfrac{{17}}{3}.\dfrac{1}{{37}}$$\,+ \dfrac{{17}}{3}.\dfrac{1}{{37}} - \dfrac{{17}}{3}.\dfrac{1}{{49}}$

$= \dfrac{{17}}{3}.\dfrac{1}{7} - \dfrac{{17}}{3}.\dfrac{1}{{49}} = \dfrac{{17}}{3}\left( {\dfrac{1}{7} - \dfrac{1}{{49}}} \right)$

$= \dfrac{{17}}{3}.\left( {\dfrac{7}{{49}} - \dfrac{1}{{49}}} \right) = \dfrac{{17}}{3}.\dfrac{6}{{49}} = \dfrac{{34}}{{49}}$

$B = \dfrac{{39}}{{7.16}} + \dfrac{{65}}{{16.31}} + \dfrac{{52}}{{31.43}} + \dfrac{{26}}{{43.49}}$

$= \dfrac{{39}}{9}.\dfrac{9}{{7.16}} + \dfrac{{65}}{{15}}.\dfrac{{15}}{{16.31}}$$\,+ \dfrac{{52}}{{12}}.\dfrac{{12}}{{31.43}} + \dfrac{{26}}{6}.\dfrac{6}{{43.49}}$

$= \dfrac{{13}}{3}.\left( {\dfrac{1}{7} - \dfrac{1}{{16}}} \right) + \dfrac{{13}}{3}.\left( {\dfrac{1}{{16}} - \dfrac{1}{{31}}} \right)$$\,+ \dfrac{{13}}{3}.\left( {\dfrac{1}{{31}} - \dfrac{1}{{43}}} \right)$$\,+ \dfrac{{13}}{3}.\left( {\dfrac{1}{{43}} - \dfrac{1}{{49}}} \right)$

$= \dfrac{{13}}{3}.\dfrac{1}{7} - \dfrac{{13}}{3}.\dfrac{1}{{16}} + \dfrac{{13}}{3}.\dfrac{1}{{16}}$$\,- \dfrac{{13}}{3}.\dfrac{1}{{31}} + \dfrac{{13}}{3}.\dfrac{1}{{31}} - \dfrac{{13}}{3}.\dfrac{1}{{43}}$$\, + \dfrac{{13}}{3}.\dfrac{1}{{43}} - \dfrac{{13}}{3}.\dfrac{1}{{49}}$

$= \dfrac{{13}}{3}.\dfrac{1}{7} - \dfrac{{13}}{3}.\dfrac{1}{{49}}$$\, = \dfrac{{13}}{3}.\left( {\dfrac{1}{7} - \dfrac{1}{{49}}} \right)$

$= \dfrac{{13}}{3}.\left( {\dfrac{7}{{49}} - \dfrac{1}{{49}}} \right) = \dfrac{{13}}{3}.\dfrac{6}{{49}} = \dfrac{{26}}{{49}}$ 

$\Rightarrow \dfrac{A}{B} = \dfrac{{34}}{{49}}:\dfrac{{26}}{{49}} = \dfrac{{34}}{{49}}.\dfrac{{49}}{{26}} = \dfrac{{17}}{{13}}$