Question

The perimeter of a rectangle is 480 cm. If its length is increased by 5% and width is decreased by 10%, the perimeter remains unchanged. What is the length of the rectangle?

Answer 1

Answer:

Step-by-step explanation:

given, perimeter of rectangle = 480 cm ,

Let length of rectangle is L and breadth is B.

perimeter of rectangle = 2(length + breadth) ,

480cm = 2(L + B),

240=L+B, ......... 1,

According to the question:

length is increased by 5%,

=L+5% of L,

L+L/5,

1.05L.

Breadth of rectangle is decreased by 10% ,

so, new breadth of rectangle = B - 10% B ,

= B - 10B/100,

= 0.9B.

Now, new perimeter of rectangle is,

2(1.05L+0.9B),

But according to question,

initial perimeter of rectangle = final perimeter of rectangle,

480=2(1.05L+0.9B),

1.05L+0.9B= 480/2=240,......2,

Comparing equation (1) and (2),

L+B=1.05L+0.9B,

1.05L-L=B-0.9B,

0.05L=0.1B,

B=0.05L÷0.1,

B=0.5L,........3,

Now substitute the value of B into equation (1),

L+0.5L=240,

1.5L=240,

L=240÷1.5,

L=160 cm,

Now, substitute value of L into equation (3),

B=0.5(160),

B=80 cm,

So orignal rectangle had L = 160cm and B= 80cm ,

The length and breadth of new rectangles can be calculated as follows,

L=1.05L,

L=1.05(160),

L=168.

B=0.9B,

B=0.9(80).

B=72.

So,in original rectangle:

Length:160 cm,

Width:80 cm,

And,in new rectangle:

Length:168 cm,

Width:72 cm.

Verification:

Perimeter is same for both rectangles:

2(L+B)=2(L+B),

2(160+80)=2(168+72),

2(240)=2(240),

480=480,proved.

Hope it helps.