Question

Here, \[5{\text{ feet }}10{\text{ inches}}\] in centimetre.

Answer 1

Hint: In order to solve this question, we will use the correlation between the feet to inches and then inches to centimeters. First of all, we will convert the given expression into inches and then finally into centimeters. Then we will place the equivalent values in the given terms. After that we will simplify it and hence, we will get the required result.
Formula Used:
1) \[1{\text{ foot}} = 12{\text{ inches}}\]
2) \[1{\text{ inch}} = 2.54{\text{ cm}}\]

Complete answer:
The given expression is \[5{\text{ feet }}10{\text{ inches }} - - - \left( i \right)\]
And we need to change it into centimetres.
Now first of all we will convert feet into inches.
As we know that
\[1{\text{ foot}} = 12{\text{ inches}}\]
\[\therefore 5{\text{ feet}} = \left( {12 \times 5} \right){\text{ inches}}\]
On multiplying, we get
\[ \Rightarrow 5{\text{ feet}} = 60{\text{ inches}}\]
Therefore, from the equation \[\left( i \right)\] we have
\[5{\text{ feet }}10{\text{ inches }} = {\text{ 60 inches }} + {\text{ 10 inches}}\]
\[ \Rightarrow 5{\text{ feet }}10{\text{ inches }} = {\text{ 70 inches }} - - - \left( {ii} \right)\]
Now we will convert inches into centimetres.
As we know that
\[1{\text{ inch}} = 2.54{\text{ cm}}\]
Therefore, from the equation \[\left( {ii} \right)\] we have
\[{\text{70 inches}} = \left( {2.54 \times 70} \right){\text{ cm}}\]
On multiplying, we get
\[ \Rightarrow {\text{70 inches}} = 177.8{\text{ cm}}\]
Therefore, \[5{\text{ feet }}10{\text{ inches}}\] is equal to \[177.8{\text{ }}cm\]
Hence, we will get the required result.

Note:
Always remember the basic conversational relations since these are the most important step to convert the given expression. Also know the correlation between different systems of the units. You can also solve this question by converting the given expression into feet and then into centimetres by using the relations:
1) \[1{\text{ inch}} = \dfrac{1}{{12}}{\text{ foot}}\]
2) \[1{\text{ foot}} = 30.48{\text{ cm}}\]
We are given: \[5{\text{ feet }}10{\text{ inches}}\]
So, \[10{\text{ inch}} = \dfrac{{10}}{{12}}{\text{ feet}}\]
Therefore, \[5{\text{ feet }}10{\text{ inches }} = {\text{ }}5{\text{ feet }} + {\text{ }}\dfrac{{10}}{{12}}{\text{ feet}}\]
On solving, we get
\[ \Rightarrow 5{\text{ feet }}10{\text{ inches = }}\dfrac{{60 + 10}}{{12}}{\text{ feet}}\]
\[ \Rightarrow 5{\text{ feet }}10{\text{ inches = }}\dfrac{{70}}{{12}}{\text{ feet}}\]
Now, convert it into the cm
Therefore, we get
\[ \Rightarrow 5{\text{ feet }}10{\text{ inches = }}\dfrac{{70}}{{12}}{\text{ }} \times {\text{30}}{\text{.48cm}}\]
\[ \Rightarrow 5{\text{ feet }}10{\text{ inches = }}177.{\text{8cm}}\]
Hence, we get the required result.