Perimeter =48 m Let the length be π‘₯ m and the breadth be 𝑦 m As we know, Perimeter =2(π‘₯+𝑦)=48 -> x+y=24 π‘₯+𝑦=24 [β‹―(1)] Area=135 m2. As we know, Area=𝑙𝑏 Therefore, 135 m^2 =π‘₯𝑦 [β‹―(2)]

Stacy Barr

Stacy Barr

Answered question

2022-09-26

Perimeter =48 m
Let the length be π‘₯ m and the breadth be 𝑦 m
As we know, Perimeter =2(π‘₯+𝑦)=48 β‡’ x + y = 24 π‘₯+𝑦=24 [β‹―(1)]
Area=135 m 2 .
As we know, Area=𝑙𝑏
Therefore, 135 m 2 =π‘₯𝑦 [β‹―(2)]

Answer & Explanation

crearti2d4

crearti2d4

Beginner2022-09-27Added 9 answers

x + y = 24
x β‹… y = 135
Now solve for 𝑦 and substitute into the other equation.
y = 24 βˆ’ x
x ( 24 βˆ’ x ) = 135
βˆ’ x 2 + 24 x βˆ’ 135 = 0
x 2 βˆ’ 24 x + 135 = 0
( x βˆ’ 15 ) ( x βˆ’ 9 ) = 0
x = 15 or x = 9
Plugging back into original equation you will get x = 15 , y = 9 or x = 9 , y = 15. It is a rectangle, therefore they can be used interchangeably. Since we can easily rotate the rectangle to alter perspective, what we define as length or breadth is arbitrary.

saucletbh

saucletbh

Beginner2022-09-28Added 3 answers

( x βˆ’ y ) 2 = ( x + y ) 2 βˆ’ 4 x y = ( 24 ) 2 βˆ’ 4.135 = 576 βˆ’ 540 = 36
Hence, ( x βˆ’ y ) = 6

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