Question

A length and breadth of a rectangular park are in the ratio of 5:2. A 2.5 wide path running around the outside of the park has an area of 305 m² find the dimensions of the park.

@Aparna​

Answer 1

Answer:

begin mathsize 16px style Let space the space length space of space the space park space equals space 5 straight a space

breadth space equals space 2 straight a space

Therefore comma space

Area space of space the space rectangular space park space equals space 5 straight a space cross times space 2 straight a space equals space 10 straight a squared

Width space of space the space path space equals space 2.5 space straight a

Outer space length space PQ space equals space 5 straight a space plus 2.5 space plus space 2.5 space equals space 5 straight a space plus 5

Outer space length space QR space equals space 2 straight a space plus 2.5 space plus space 2.5 space equals space 2 straight a space plus 5

Area space of space PQRS space equals space left parenthesis 5 straight a space plus 5 right parenthesis space left parenthesis 2 straight a space plus 5 right parenthesis equals space 10 straight a squared space plus space 35 space straight a space plus space 25

Area space of space the space path space equals space open square brackets open parentheses 10 straight a squared space plus space 35 space straight a space plus space 25 close parentheses space minus space 10 straight a squared close square brackets

rightwards double arrow space 305 space equals space 35 straight a space plus space 25

rightwards double arrow straight a space equals space 280 over 35 space equals space 8

Therefore comma

length space of space the space park space equals space 5 straight a space equals space 5 space cross times space 8 space equals space 40 space straight m

breadth space of space the space park space equals space 2 straight a space equals space 2 space cross times space 8 space equals space 16 space straight m

end style

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Answer 2

Solution :

$\underline{\bf{Given\::}}}}$

• Length & breadth of a rectangular park are in the ratio = 5 : 2
• 2.5 m wide path of a rectangular park outside.
• Area of the rectangular park = 305 m²

$\underline{\bf{To\:find\::}}}}$

The dimensions of the park .

$\underline{\bf{Explanation\::}}}}$

Let the ratio of the rectangular park be r

$\bullet\:\sf{Length\:of\:rectangular\:park=5r}\\\bullet\sf{Breadth\:of\:rectangular\:park=2r}$

$\bigstar$2.5 m wide path which are running around the outside of park, so;

$\bullet\:\sf{Outside\:length\:of\:rectangular\:park=5r+2.5m+2.5m}\\\bullet\sf{Outside\:breadth\:of\:rectangular\:park=2r+2.5m+2.5m}$

A/q

We know that fromula of the area of rectangle :

$\boxed{\bf{Area\:_{(rectangle)}=Length\times breadth\:\:\:\:(sq.unit)}}}$

$\longrightarrow\sf{Area\:_{(path)}=Area\:_{(outer\:side)}-Area\:_{(park)}}\\\\\longrightarrow\sf{305=(5r+2.5+2.5)(2r+2.5+2.5)-(5r\times 2r)}\\\\\longrightarrow\sf{305=(5r+5)(2r+5)-10r^{2}}\\\\\longrightarrow\sf{305=10r^{2}+25r+10r+25-10r^{2}}\\\\\longrightarrow\sf{305=\cancel{10r^{2}}+35r+25 \cancel{-10r^{2}}}\\\\\longrightarrow\sf{305=35r+25}\\\\\longrightarrow\sf{35r=305-25}\\\\\longrightarrow\sf{35r=280}\\\\\longrightarrow\sf{r=\cancel{280/35}}\\\\\longrightarrow\bf{r=8\:m}$

Thus;

$\boxed{\bf{D\:\:I\:\:M\:\:E\:\:N\:\:S\:\:I\:\:O\:\:N\:\:'S\::}}}$

$\bullet\:\sf{Length\:of\:rectangular\:park=5r=(5\times 8)=\boxed{\bf{40\:m}}}\\\\\bullet\sf{Breadth\:of\:rectangular\:park=2r=(2\times 8)=\boxed{\bf{16\:m}}}$