Question

the area pf rectangle is 300cm^2 and its length and breadth are in the ratio 3:4 . Find the length of its diognals​

Answer 1

Answer:

$25cm$

Step-by-step explanation:

let its length is 3x

and its breadth is 4x

so, area of rectangle is

3x*4x=300

$12 {x}^{2} = 300$

${x}^{2} = 25$

$x = 5$

so, length and breadth is 15 and 20 respectively

so, lengths of diagonal is

$\sqrt{ {15}^{2} + {20}^{2} }$

$= \sqrt{225 + 400}$

$\sqrt{625}$

$= 25$

Answer 2

Answer:

Given :

$\sf{Area\:of \:the \:rectangle = {300}^{2}}$

$\sf{Ratio\: of \:the\: Lenght \:and\: Breadth = 3:4}$

To find :

$\sf{Lenght \:of\: the\: diagonals }$

Taken :

$\sf{Area \:of\: the \:rectangle\: :}$

$\bold{\sf{\boxed{A=L\:\times\:B}}}$

$\sf{Where,}$

$\sf{A=Area\: of\: the \:rectangle}$

$\sf{L=Length}$

$\sf{B=Breadth}$

Concept :

Let the ratio be x . So , the ratio of Length be 3x and Breadth be 4x .

Solution :

$\sf{:\implies{{300cm}^{2}=3x\times4x}}$

$\sf{:\implies{{300cm}^{2}={12x}^{2}}}$

$\sf{:\implies{\dfrac{{300cm}^{2}}{12}={x}^{2}}}$

$\sf{:\implies{25 cm = {x}^{2}}}$

So , the lenght of the diagonal is 25 cm .

Extra information :

To find Lenght and Breadth . Solve after the equation .

$\sf{:\implies{25 cm = {x}^{2}}}$

$\sf{:\implies{\sqrt{25 cm} = x}}$

$\sf{:\implies{5 cm = x }}$

▪︎ Length -:

$\sf{:\implies{L = 5 × 3 }}$

$\sf{:\implies{L = 15 cm}}$

So , the length of the rectangle is 15 cm .

▪︎ Breadth -:

$\sf{:\implies{B = 5 × 4}}$

$\sf{:\implies{B = 20 cm}}$

So , the breadth of the rectangle is 20 cm .

Answer :

So , the lenght of the diagonal is 25 cm .