Question

The Length of Rectangle is twice its breadth.If its length is decreased by 4cm and breadth is increased by 4cm, the area of the rectangle increased by $52cm^2$. The length of the rectangle is?

• A. 68 cm
• B. 17 cm
• C. 34 cm
• D. 48 cm

Answer 1

Answer:

C. 34 cm

Length L = 2B

Let Breadth B= x

then L = 2x

New Length L₁= 2x-4

New breadth B₁= x+4

New Area A₁=52 +A

Area of Rectangle old $A=L\times{B}=2x\times{x}=2x^2$

New Area $A_1=(2x-4)\times(x+4)$

$A_1=2x^2+8x-4x-16$

$A_1=2x^2+4x-16$

We Know $A_1=52+A=52+2x^2$

then ., $2x^2+4x-16=52+2x^2$

$4x-16=52$

$4x=68$

$x=17$

Original Length of Rectangle $L=2x=2\times{17}=34cm$