Question

A picture is painted on a ceiling of a marriage hall whose length and breadth are 18m and 7 m . There is a border of 10cm along each of its sides. Find the area of the border​

Answer 1

Hint: Here the picture on a ceiling of marriage hall has length and the breadth; it means we can assume that the ceiling is a rectangular shape so the area of the rectangle is taken as the product of length and breadth, here it is asked to find the area of the border so, we have to subtract the area of the total ceiling space with border and area of the ceiling space without border.

Complete step-by-step answer:

The length of the picture on a ceiling of marriage hall is \[l = 18\;{\rm{m}}\]
The breadth of the picture on a ceiling of marriage hall is\[b = 7\;{\rm{m}}\]
The border of the picture is
\[
\Rightarrow x = 10\;{\rm{cm}}\, \times \dfrac{{1\,{\rm{m}}}}{{100\,{\rm{cm}}}}\\
 = 0.1\;{\rm{m}}
\]
Then, the length of the picture on a ceiling of marriage hall with border is
\[
\Rightarrow {l_1} = 18\;{\rm{m}} + {\rm{0}}{\rm{.1}}\,{\rm{m}} + {\rm{0}}{\rm{.1}}\,{\rm{m}}\\
{\rm{ = 18}}{\rm{.2}}\,{\rm{m}}
\]
Then, the breadth of the picture on a ceiling of marriage hall with border is
\[
\Rightarrow {b_1} = 7\;{\rm{m}} + {\rm{0}}{\rm{.1}}\,{\rm{m}} + {\rm{0}}{\rm{.1}}\,{\rm{m}}\\
{\rm{ = 7}}{\rm{.2}}\,{\rm{m}}
\]
The equation to find the area of the border itself is,
\[\Rightarrow a = \left( {{l_1} \times {b_1}} \right) - (l \times b)\]
Substitute the values in the above equation.
\[
\Rightarrow a = \left( {{l_1} \times {b_1}} \right) - (l \times b)\\
 = (18.2\,{\rm{m}} \times 7.2\,{\rm{m}}) - (18\,{\rm{m}} \times 7\,{\rm{m}})\\
 = 131.04 - 126\\
 = 5.04\;{{\rm{m}}^{\rm{2}}}
\]
Therefore, the area of the border is \[5.04\;{{\rm{m}}^{\rm{2}}}\].

Note: Here, the question is about to find the area of the border, be clear about the point, the border is the extra distance that added to the picture length and the breadth, so we have to subtract the picture area from the whole area. Before solving the problem check that all the units are in equal format else the answer will be wrong. (if the length is in meters then the breadth should be meters, or length is in centimeter then the breadth should be in centimeters and the border width too.)