Question

a rectangular grassy lawn measuring 48 by 35 is to be surrounded externally by a path which is 2.5 metre wide find the cost of levelling the path rate Rupees 4.50 per square metre​

Answer 1

$\huge\mathbb{SOLUTION:-}$

$\bold{Given:-}\begin{cases}\sf{Length\:of\:lwan(l)=48m}\\ \sf{Breadth\: of\: lwan=35m}\\ \sf{width\:of\:path=2.5m}\end{cases}$

• Now first find area of grassy Lawn

• which is in the form of rectangle So area of rectangle

$\boxed{\sf{Area\:of\: rectangle=length\times breadth}}$

$\bf\underline{\red{According\:to\: Question:-}}$

$\sf\implies Area\:of \:lwan=48m\times 35m\\ \\ \sf\implies Area\:of\:lwan= 1680m{}^{2}$

$\boxed{\sf{Area\:of\: lawn=1680m{}^{2}}}$

• Now the path is built around it

• New length =48+2.5=50.5m

• New breadth=35+2.5= 37.5m

Now new area of lawn

$\begin{cases}\sf{New\:Length\:of\:lwan(l)=50.5m}\\ \sf{New\:Breadth\: of\: lwan=37.5m}\end{cases}$

$\sf\implies New\:area\:of\: lawn =50.5m\times 37.5m\\ \\ \sf\implies New\:area\:of\: lawn=1893.75m{}^{2}$

$\boxed{\sf{New\:area\:of\: lawn=1893.75m{}^{2}}}$

• Now we have to find the area of path

• If we subtract the area of lawn from new area of lawn we get the area of path

$\sf\implies Area\:of\:path=1893.75-1680\\ \\ \sf\implies Area\:of\:path=264.25m{}^{2}$

$\boxed{\sf{\green{Area\:of\:path=213.75m{}^{2}}}}$

• The cost of leveling the path isRs.4.50

$\tt\mapsto Cost\:of\: lavelling \:1\:m=4.50Rs\\ \\ \tt\mapsto Cost\:of\: levelling \:213.75m{}^{2}=4.50\times 213.75\\ \\ \tt\implies cost\:of\: lavelling=961.875Rs$

$\boxed{\sf{\purple{Cost\:of\: levelling\:the\:path=961.875\:Rs.}}}$

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Answer 2

Answer:

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