Question

the length of a rectangle is 5 cm more than its breadth if the length is increased by 6 cm and breadth is decreased by 3 cm then the new perimitter becomes 8 by 7 of the original perimeter find the length and breadth of the original rectangle.

Answer 1

let breadth is x then length is (X+5)
perimeter = 2( l+b) =2( X+X+5) = 2(2x+ 5) = 4x+10
according to question
new length = X+5+6 = X+11
new breadth = x-3
new perimeter = 2( X+11+x-3) = 2 ( 2x+ 8) = 4x+ 16
given that
8/7(4x+10) = (4x+16)
32x+ 80 = 28x+112
4x = 32
X = 8
breadth = 8:cm
length = 8+5=13 cm

Answer 2

Answer:

The length and breadth of the original rectangle is 13 cm and 8 cm respectively .

Step-by-step explanation:

Let the original breadth be x

We are given that the length of a rectangle is 5 cm more than its breadth

So, original length = x+5

Perimeter of rectangle = $2(l+b)=2(x+5+x)=2(2x+5)=4x+10$

Now the length is increased by 6 cm and breadth is decreased by 3 cm

New length = x+5+6=x+11

New breadth = x-3

Perimeter of new rectangle = $2(l+b)=2(x+11+x-3)=2(2x+8)=4x+16$

We are given that  the new perimeter becomes 8 by 7 of the original perimeter

$4x+16=\frac{8}{7}(4x+10)$

$28x+112=(32x+80)$

$32=4x$

$8=x$

So, original breadth = 8 cm

Original length = x+5=8+5=13 cm

Hence the length and breadth of the original rectangle is 13 cm and 8 cm respectively .