Answer:
a.[tex]\sqrt{52}[/tex]cm or 7.21cm
b.[tex]\sqrt{170}[/tex]cm or 13.04cm
c. x= [tex]\sqrt{136}[/tex]cm or 11.66cm, y=[tex]\sqrt{191}[/tex]cm or 13.82cm
Step-by-step explanation:
a. You have to find the length of the other two sides of the triangle using the information already given. The first side is 6cm and the other is 12-9=4cm. Because it's a right-angled triangle you can use pythagoras
[tex]c^2=a^2+b^2\\x^2=6^2+4^2\\x^2=36+16\\x^2=52\\x=\sqrt{52}cm \\x=7.21cm[/tex]
b. You can use pythagoras again because it's a right-angle triangle
[tex]x^{2} =7^2+11^2\\x^2=170\\x=\sqrt{170} cm\\ = 13.04cm[/tex]
c. In this question you have to find x and y. We need to find x first using pythagoras
[tex]x^2=6^2+10^2\\x^2=136\\x=\sqrt{136}cm \\=11.66cm[/tex]
Now that we've found x we can find y using pythagoras but instead of find c, we will find another side
[tex]c^2=a^2+b^2\\19^2=\sqrt{170} ^2 + b^2\\361=170+b^2\\361-170=170+b^2-170\\191=b^2\\b=\sqrt{191}cm \\=13.82cm[/tex]
Hope this helps :)
