Từ D kẻ đường vuông góc DK (K thuộc AB)  \(\Rightarrow CDKH\) là hình chữ nhật

\(\Rightarrow\left\{{}\begin{matrix}HK=CD=3,5\left(m\right)\\CH=DK=5\left(m\right)\end{matrix}\right.\)

Ta có:\(\widehat{KDA}=135^0-90^0=45^0\)  

Trong tam giác vuông BCH:

\(cos\widehat{BCH}=\dfrac{CH}{BC}\Rightarrow BC=\dfrac{CH}{cos\widehat{BCH}}=\dfrac{5}{cos30^0}=\dfrac{10\sqrt{3}}{3}\left(m\right)\)

\(\Rightarrow BH=\sqrt{BC^2-CH^2}=\dfrac{5\sqrt{3}}{3}\left(m\right)\)

Trong tam giác vuông ADK:

\(\widehat{KAD}=90^0-\widehat{KDA}=45^0\Rightarrow\widehat{KAD}=\widehat{KDA}\Rightarrow\Delta ADK\) vuông cân tại K

\(\Rightarrow AK=DK=5\left(m\right)\)

\(\Rightarrow AD=\sqrt{AK^2+DK^2}=5\sqrt{2}\left(m\right)\)

\(AB=BH+HK+KA=\dfrac{51+10\sqrt{3}}{6}\left(m\right)\)

Chu vi: \(AB+CD+BC+AD\approx27,7\left(m\right)\)

Diện tích: \(S=\dfrac{1}{2}\left(AB+CD\right).CH\approx37,2\left(m^2\right)\)

a) \(k=-5\)

b) 

Tìm x xong rồi tìm y

3 thì làm kiểu gì cũng được

Bài 3:

Hình 1:

Xét ΔABC có \(\widehat{A}+\widehat{B}+\widehat{C}=180^0\)

=>\(x+60^0+40^0=180^0\)

=>\(x=180^0-100^0=80^0\)

Hình 2:

Xét ΔABD có \(\widehat{ADC}\) là góc ngoài tại đỉnh D

nên \(\widehat{ADC}=\widehat{ABD}+\widehat{BAD}=110^0\)

=>\(y=110^0\)

ΔDAC cân tại D

=>\(\widehat{DAC}=\widehat{DCA}=\dfrac{180^0-\widehat{ADC}}{2}\)

=>\(x=\dfrac{180^0-110^0}{2}=35^0\)

Hình 3:

Ta có: \(\widehat{CAB}+60^0=180^0\)

=>\(\widehat{CAB}=180^0-60^0=120^0\)

Xét ΔCAB có \(\widehat{CAB}+\widehat{ABC}+\widehat{ACB}=180^0\)

=>\(x+2x+120^0=180^0\)

=>\(3x=60^0\)

=>\(x=20^0\)

Hình 4:

Ta có: \(\widehat{ADC}+\widehat{ADB}=180^0\)

=>\(\widehat{ADB}=180^0-80^0=100^0\)

Xét ΔADB có

\(\widehat{ADB}+\widehat{ABD}+\widehat{BAD}=180^0\)

=>\(x+60^0+100^0=180^0\)

=>\(x=20^0\)

ta có: \(\widehat{ACD}+135^0=180^0\)

=>\(\widehat{ACD}=180^0-135^0=45^0\)

Xét ΔACD có \(\widehat{ACD}+\widehat{ADC}+\widehat{DAC}=180^0\)

=>\(y+80^0+45^0=180^0\)

=>\(y=55^0\)

\(=\left(\dfrac{\sqrt{5}\left(\sqrt{3}-2\right)}{\sqrt{3}-2}+\dfrac{\sqrt{6}\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{3}+\sqrt{2}}-\dfrac{\sqrt{6}-\sqrt{5}}{\left(\sqrt{6}-\sqrt{5}\right)\left(\sqrt{6}+\sqrt{5}\right)}\right):\sqrt{\dfrac{5}{2}}\)

\(=\left(\sqrt{5}+\sqrt{6}-\sqrt{6}+\sqrt{5}\right):\dfrac{\sqrt{5}}{\sqrt{2}}\)

\(=2\sqrt{5}.\dfrac{\sqrt{2}}{\sqrt{5}}=2\sqrt{2}\)

a) Ta có: \(\left(\dfrac{\sqrt{15}-\sqrt{20}}{\sqrt{3}-2}+\dfrac{3\sqrt{2}+2\sqrt{3}}{\sqrt{3}+\sqrt{2}}-\dfrac{1}{\sqrt{6}+\sqrt{5}}\right):\sqrt{\dfrac{5}{2}}\)

\(=\left(\sqrt{5}+\sqrt{6}-\sqrt{6}+\sqrt{5}\right):\dfrac{\sqrt{10}}{2}\)

\(=2\sqrt{5}\cdot\dfrac{2}{\sqrt{10}}=2\sqrt{2}\)

\(\dfrac{x}{27}=\dfrac{2}{9}-\dfrac{1}{3}\Rightarrow\dfrac{x}{27}=-\dfrac{1}{9}\Rightarrow\dfrac{x}{27}=\dfrac{-3}{27}\Rightarrow x=27\)

\(\dfrac{x}{27}=\dfrac{2}{9}-\dfrac{1}{3}=-\dfrac{1}{9}\Rightarrow x=-\dfrac{1}{9}.27=-3\).

\(S=\left(1-\dfrac{1}{2}\right)\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{4}\right).....\left(1-\dfrac{1}{2022}\right)\left(1-\dfrac{1}{2023}\right)\)

\(=\dfrac{1}{2}.\dfrac{2}{3}.\dfrac{3}{4}....\dfrac{2022}{2023}\)

\(=\dfrac{1.2.3....2022}{2.3.4....2023}\)

\(=\dfrac{1}{2023}\)

\(y:2+y.0,75=15,34-14,09\)
\(y.0,5+y.0,75=1,25\)
\(y.\left(0,5+0,75\right)=1,25\)
\(y.1,25=1,25\)
\(y=1\)
Chú ý:Dấu \(.\) là dấu nhân nha.