The perimeter of a rectangular plot is 32 m. If the length l is increased by 2 m and the breadth b is decreased by 1m,
The perimeter of a rectangular plot is 32 m. If the length l is increased by 2 m and the breadth b is decreased by 1m, the area of the plot remains the same. Then the values of l and b are respectively.
A) 6m, 10m
B) 10m, 6m
C) 10m, 10m
D) 6m, 6m
2 Answers
Correct option is (B) 10m, 6m
\(2(l+b)=32\) \((\because\) Perimeter = 32 m (given))
\(\Rightarrow l+b=\frac{32}2=16\) __________(1)
Area of rectangular plot \(=lbm^2\)
After increasement in \(l\) by 2 m and decreasement in b by 1 m the area of plot remains same.
\(\therefore(l+2)(b-1)=lb\)
\(\Rightarrow lb+2b-l-2=lb\)
\(\Rightarrow -l+2b=2\) __________(2)
By adding equations (1) & (2), we get
3b = 16+2 = 18
\(\Rightarrow b=\frac{18}3=6\)
\(\therefore l=16-b\)
= 16 - 6 = 10 m
Hence, \(l\;and\;b\) are respectively \(l\) = 10 m & b = 6 m.