Answer:
Step-by-step explanation:
1.) [tex]c = \sqrt{a^{2} +b^{2} }[/tex]
a = 10, b = 7, c = x?
10+7= x
[tex]10^{2} + 7^{2} =x^{2}[/tex]
100 + 49 = [tex]x^{2}[/tex]
149 = [tex]x^{2}[/tex]
[tex]\sqrt{149} =[/tex] 12.206...
x = 12.2
2.) x + 19 = 21
[tex]x^{2} + 19^{2} =21^{2}\\21^{2}-19^{2} = x^{2}[/tex]
441 - 361 = [tex]x^{2}[/tex]
80 = [tex]x^{2}[/tex]
[tex]\sqrt{80}[/tex] = 8.94
x = 9
3.) x + 16 = 27
[tex]x^{2} + 16^{2}= 27^{2} \\27^{2} -16^{2} =x^{2}[/tex]
729 - 256 = [tex]x^{2}[/tex]
473 = [tex]x^{2}[/tex]
[tex]\sqrt{473}[/tex] = 21.74
x = 21.7
4.) 12.8 + 5.3 = x
[tex]12.8^{2} + 5.3^{2} =x^{2} \\163.84 + 28.09 = x^{2}\\191.93 = x^{2} \\\sqrt{191.93} = 13.85\\x = 13.9[/tex]
8.) x = 11.48 ft
a = 3.5 ft
, b = x=?
, c = 12 ft
[tex]3.5^{2} + x^{2} =12^{2} \\12.25 +x^{2} =144\\144-12.25=x^{2} \\131.75 = x^{2} \\\sqrt{131.75} =11.48\\x = 11.48[/tex]
9.) x = 32.078 feet
[tex]14^{2} +x^{2} =35^{2}\\196 + x^{2} =1225\\1029 = x^{2} \\\sqrt{1029} = 32.078 ft\\x = 32.078 ft\\[/tex]
10.) perimeter = 31.96
hope this helped a lot
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