Question

1 poir
When 4 is Subtracted from length and breadth of the rectangle, the
perimeter becomes 24; what is the mathematical form of the Statement?​

Answer 1

Answer:

perimeter ( p ) =2× length ( l ) +2× breadth ( b )

or,

p=2l+2b

We can substitute the values from the statement into this formula to obtain a mathematical expression for the statement.

26=2(l−5)+2(b−5)

As there are two unknowns in this equation, there is no way to solve it for the original length and breadth, but we can rearrange it so that one of terms is the subject:

2(l−5)+2(b−5)=26

2(l−5)=26−2(b−5)

l−5=26−2(b−5)2

l−5=13−b+5

l−5=18−b

l=18−b+5

l=23−b

We now have an equation which we can use to easily find length if we later know the original breadth. Similarly, we can then rearrange it to be able to find breadth should we later know the original length:

l=23−b

l+b=23

b=23−l

To check that our equations are accurate, we can substitute an arbitrary value. Say the breadth of the rectangle is 5. We could find the length using our formula:

l=23−b=23−5=18

Now that we know the length and breadth, we can check that our formula is correct by substituting these values into the equation p=2(l−5)+2(b−5) and make sure we get 26 .

p=2(l−5)+2(b−5)

p=2(18−5)+2(5−5)

p=2(13)+2(0)

p=26

We have now expressed the statement in mathematical terms and checked that the statement is accurate.