Answer:
1. [tex]x=13,\,y=13\sqrt{2}[/tex]
2. [tex]x=y=\frac{30\sqrt{2}}{2}[/tex]
3. [tex]x=6,\,y=3\sqrt{3}[/tex]
4. [tex]x=17\sqrt{3},\,y=17[/tex]
5. [tex]x=y=10[/tex]
6. [tex]x=50,\,y=25[/tex]
7. [tex]x=y=2\sqrt{7}\,\,(\mathrm{because}\,\,\frac{2\sqrt{14}}{\sqrt{2}} = \frac{2\sqrt{2}\sqrt{7}}{\sqrt{2}} = 2\sqrt{7} )[/tex]
8. [tex]y = \frac{24\sqrt{3}}{3} = 8\sqrt{3},\,x = 16\sqrt{3}[/tex]
9. [tex]x = 11\sqrt{3},\,y=11\sqrt{3}\cdot\sqrt{3} = 33[/tex]
10. [tex]y = 2\sqrt{6},\,x = \sqrt{6}\cdot\sqrt{3} = 3\sqrt{2}[/tex]
11. [tex]x = \sqrt{10},\,y=\sqrt{10}*\sqrt{2} = 2\sqrt{5}[/tex]
12. [tex]x = \frac{4\sqrt{21}}{\sqrt{3}} = 4\sqrt{7},\,y=8\sqrt{7}[/tex]
13. [tex]x = 17\sqrt{3},\,z = 34,\,y =34\sqrt{2}[/tex]
14. [tex]x = 27\cdot\frac{2}{\sqrt{3}}=18\sqrt{3},\,h=9\sqrt{3},\,z=9,\,y=18[/tex]
Step-by-step explanation:
Please ask for explanation on specific numbers, as doing it all is a lot of writing. From the parially-written aswers I assume you know the rules for 90-45-45 triangles and 90-60-30 triangles, which are the only ones in the task sheet.
