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The first, second and fourth terms of the proportion are 9, 21, 77. Find the third term.
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The first, second and fourth terms of the proportion are 9, 21, 77. Find the third term.
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Verified answer
[tex]\large{\clubs \: {\underline{\underline{\sf{We \: \: Know:-}}}}}[/tex]
Now,
[tex]\large{\mapsto{\sf{\dfrac{9}{21} = \dfrac{x}{77}}}}[/tex]
[tex]\large{\mapsto{\sf{9 \times 77 = 21 \times x}}}[/tex]
[tex]\large{\mapsto{\sf{693 = 21x}}}[/tex]
[tex]\large{\mapsto{\sf{\dfrac{\cancel{693}}{\cancel{21}} = x}}}[/tex]
[tex]\large{\mapsto{\sf{33 = x}}}[/tex]
[tex]\large{\gray{\underline{\boxed{\sf{\therefore{Answer = 33}}}}}}[/tex]
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ʚїɞ The Third Term Is 33
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Answer:
[tex]\qquad\qquad\boxed{{ \: \bf \: Third\:term \: = \: 33 \: }}\\ \\ [/tex]
Step-by-step explanation:
Given that, The first, second and fourth terms of the proportion are 9, 21, 77.
Let assume that third term be x.
So,
[tex]\sf\implies \sf \: 9,21,x,77 \: are \: in \: proportion. \\ \\ [/tex]
[tex]\sf\implies \sf \: 9 : 21 :: x : 77 \\ \\ [/tex]
[tex]\qquad\sf \: \dfrac{9}{21} = \dfrac{x}{77} \\ \\ [/tex]
[tex]\qquad\sf \: \dfrac{3}{7} = \dfrac{x}{77} \\ \\ [/tex]
[tex]\qquad\sf \: x = 77 \times \dfrac{3}{7} \\ \\ [/tex]
[tex]\qquad\sf \: x = 11 \times 3 \\ \\ [/tex]
[tex]\qquad\sf\implies \sf \: x = 33 \\ \\ [/tex]
Hence,
[tex]\sf\implies \sf \: Third\:term \: = \: 33 \\ \\ [/tex]
[tex]\rule{190pt}{2pt}[/tex]
Additional Information
1. Alternendo
[tex]\sf \:If\:\dfrac{a}{b} = \dfrac{c}{d} ,\:then \: \bf \: \dfrac{a}{c} = \dfrac{b}{d} \\ \\ [/tex]
2. Invertendo
[tex]\sf \:If\:\dfrac{a}{b} = \dfrac{c}{d} ,\:then \: \bf \: \dfrac{b}{a} = \dfrac{d}{c} \\ \\ [/tex]
3. Componendo
[tex]\sf \:If\:\dfrac{a}{b} = \dfrac{c}{d} ,\:then \: \bf \: \dfrac{a + b}{b} = \dfrac{c + d}{d} \\ \\ [/tex]
4. Dividendo
[tex]\sf \:If\:\dfrac{a}{b} = \dfrac{c}{d} ,\:then \: \bf \: \dfrac{a - b}{b} = \dfrac{c - d}{d} \\ \\ [/tex]