Question

Perimeter of a rectangle is p and its diagonal

d. Find the difference of its length and breath

Answer 1

(l^2 + b^2)^(1/2) = d

l^2 + b^2 = d^2

2(l+b)=p

l + b = p/2

(l+b)^2 +(l-b)^2 = 2(l^2 + b^2)

(l-b)^2 = 2d^2 - p^2/4

l-b = (2d^2 - p^2/4)^(1/2)

i hope this is the answer

Answer 2

Answer:

The difference between length and breadth is  $l-b=\frac{\sqrt{8d^2-p^2}}{2}$

Step-by-step explanation:

Given : Perimeter of a rectangle is p and its diagonal  d.

To find : The difference of its length and breath ?

Solution :

Let the length and breadth be l and b respectively.

The perimeter is p and diagonal d.

The perimeter of rectangle is $p=2(l+b)$

i.e. $l+b=\frac{p}{2}$

The diagonal of rectangle be $d=\sqrt{l^2+b^2}$

i.e. $d^2=l^2+b^2$

$d^2=l^2+b^2+2lb-2lb$

$d^2=(l+b)^2-2lb$

$d^2=(\frac{p}{2})^2-2lb$

$d^2-\frac{p^2}{4}=-2lb$

We know,

$(l-b)^2=l^2+b^2-2lb$

Substitute the values,

$(l-b)^2=d^2+d^2-\frac{p^2}{4}$

$(l-b)^2=2d^2-\frac{p^2}{4}$

$(l-b)^2=\frac{8d^2-p^2}{4}$

$l-b=\frac{\sqrt{8d^2-p^2}}{2}$

Therefore, the difference between length and breadth is  $l-b=\frac{\sqrt{8d^2-p^2}}{2}$