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Find the mean proportional between
36 and 4
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Find the mean proportional between
36 and 4
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mean proportional between
mean proportional between36 and 4 is 12 .
Question :
Find the mean proportional between
36 and 4 .
Solution :
as we know that,
mean proportional of two numbers a and b = square root of their product .
i.e;
[tex] \sf \: mean \: proportional \: = \: \boxed{\sf \: \sqrt{a \: \times \: b} } \\ [/tex]
So,
[tex] \sf \: mean \: proportional \: = \: \sqrt{36 \: \times \: 4} \\ \\ = \: \sf \: \sqrt{ {(6)}^{2} \times {(2)}^{2} } \\ \\ = \sf \: 6 \: \times \: 2 \: \\ \\ \sf \: = \: 12 \\ \\ [/tex]
therefore, mean proportional between
mean proportional between36 and 4 is 12 .
[tex] \\ [/tex]
Verified answer
Answer:
[tex]\boxed{ \sf{ \: \bf \:12 \: is \: the \: mean \: proportion \: between \: 36 \: and \: 4 \: }}\\ \\ [/tex]
Step-by-step explanation:
We have to find the mean proportion between 36 and 4.
Let assume that x be the mean proportion between 36 and 4.
So, By definition of mean proportion,
[tex]\sf\implies \sf \: 36,x, 4, \: are \: in \: continued \: proportion. \\ \\ [/tex]
[tex]\sf\implies \sf \: \dfrac{36}{x} = \dfrac{x}{4} \\ \\ [/tex]
[tex]\sf \: {x}^{2} = 36 \times 4 \\ \\ [/tex]
[tex]\sf \: x = \sqrt{ 36 \times 4 }\\ \\ [/tex]
[tex]\sf \: x = \sqrt{ 3 \times 3 \times 4 \times 4 }\\ \\ [/tex]
[tex]\sf \: x = 3 \times 4 \\ \\ [/tex]
[tex]\sf\implies \bf \: x = 12 \\ \\ [/tex]
Hence,
[tex]\sf\implies \bf \:12 \: is \: the \: mean \: proportion \: between \: 36 \: and \: 4 \\ \\ [/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]