Question

The Length of Rectangle is twice its breadth.If its length is decreased by 64cm and breadth is increased by 6cm, the area of the rectangle increased by $24cm^2$. The area of the new rectangle is?

• A. 340 sqcm
• B. 346 sqcm
• C. 364 sqcm
• D. 360 sqcm

Answer 1

Answer:

C. 364 sqcm

Length L = 2B

Let Breadth B= x

then L = 2x

New Length L₁= 2x-6

New breadth B₁= x+6

New Area A₁=24 +A

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

New Area $A_1=(2x-6)\times(x+6)$

$A_1=2x^2+12x-6x-36$

$A_1=2x^2+6x-36$

We Know $A_1=24+A=24+2x^2$

then ., $2x^2+6x-36=24+2x^2$

$6x-36=24$

$6x=60$

$x=10$

Original Length of Rectangle $L=2x=2\times{10}=20cm$

Original Breadth $B=x=10cm$

$L_1=20-6=14cm$

$B_1=20+6=26cm$

New area $A_1=14\times{26}=364cm^2$