If the length of a certain rectangle is decreased by 4 cm and the width is increased by 3 cm, a square with the same area as the original rectangle would result. The perimeter of the original rectangle (in cm) is :
A. 44
B. 46
C. 48
D. 50
Answer: Option D
Solution(By Examveda Team)
Let the length and width of the rectangle be $$l$$ cm and b cm respectively.Then,
$$\eqalign{ & \left( {l - 4} \right)\left( {b + 3} \right) = lb \cr & \Rightarrow lb + 3l - 4b - 12 = lb \cr & \Rightarrow 3l - 4b = 12.....(i) \cr & {\text{And, }} \cr & l - 4 = b + 3 \cr & \Rightarrow l - b = 7.....(ii) \cr} $$
Multiplying (ii) by 4 and subtracting (i) from it, we get :
$$l$$ = 16
Putting $$l$$ = 16 in (ii), we get : b = 9
∴ Perimeter of the original rectangle :
$$\eqalign{ & = 2\left( {l + b} \right) \cr & = [2\left( {16 + 9} \right)]cm \cr & = 50\,cm \cr} $$
Related Questions on Area
A. 15360 m2
B. 153600 m2
C. 30720 m2
D. 307200 m2
E. None of these
A. 2%
B. 2.02%
C. 4%
D. 4.04%
E. None of these
A. 16 cm
B. 18 cm
C. 24 cm
D. Data inadequate
E. None of these
The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is:
A. 40%
B. 42%
C. 44%
D. 46%
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