Question

The length and breadth of a rectangular field are in the ratio $7:4$. A path $4m$ wide running all around outside it has an area of $416m^2$. Find the length and breadth of the field.

• A. $35m,20m$
• B. $28m,16m$
• C. $21m,12m$
• D. $42m,24m$

Answer 1

Answer: (B)

Let the length and breadth is $7x$ and $4x$ of the field (given ratio of length and breadth is $7:4$)

If $4m$ path is outside field made

then breadth $=4x$ and length is $7x+4+4=7x+8$

Then thje area of path $=2(4x\times 4)+2\left[\right(4x+8\left)4\right]$

But path area given $416$ sq m

Then $2(4x\times 4)+2\left[\right(4x+8\left)4\right]=416\Rightarrow 32x+56x+64=416\Rightarrow 56x=352\Rightarrow x=4$

Then length=$7\times 4=28m$ and breadth=$4\times 4=16m$