Question

In rectangle ABCD, AB = 4x - 2y. BC = x + 2y + 5. CD = 3x + y + 6. AD = 3x - y - 1 then find the length, breadth and perimeter of that rectangle. ​

Answer 1

Answer:

sorry I don't know exactly what the answer is

Answer 2

$ABCD, AB = 4x - 2y , BC = x + 2y + 5, CD = 3x + y + 6 , AD = 3x - y - 1$

Length, Breadth and Perimeter of that rectangle are $4$ units,$1$ unit and $10$ units.

Step by step explanation:

Given:

$AB = 4x - 2y \\BC = x + 2y + 5\\CD = 3x + y + 6 \\AD = 3x - y - 1$

To find:

Length, Breadth and Perimeter of the rectangle.

Perimeter of rectangle:

Perimeter of rectangle$=2(l+b)$

Opposites side of a rectangle are equal in measure

$AB=CD$ and$BC=AD$

To find ,$AB=CD$

$4x-2y=3x+y+6$

$4x-2y-3x-y-6=0$

$x-3y-6=0\cdots\cdots\cdots\ccdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots(1)$

To find, $BC=AD$

$x+2y+5=3x-y-1$

$3x-y-1-x-2y-5=0$

$2x-3y-6=0\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots(2)$

subtract equation (2) and (1)$2x-3y-6=0\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots(2)$

$x-3y-6=0\cdots\cdots\cdots\ccdots\cdots\cdots\cdots\cdots\cdots\cdots\cdots(1)$

____________

$x=0$

Put in the value of $x=0$ in equation (1)

$x-3y-6=0\\(0)-3y-6=0\\-3y=6\\y=\frac{6}{-3} \\y=-2$

therefore to substitute $x$ and $y$ value in $AB$ and $BC$

Length:

$AB=4x-2y$                                  $x=0, y=-2$

      $=4(0)-2(-2)$

      $=0+4$

$AB=4 units$

Breath:

$BC=x+2y+5$                         $x=0, y=-2$

    $=0+2(-2)+5$

    $=-4+5$

$BC= 1 unit$

hence,

        perimeter of rectangle $= 2(AB+BC)$

                                        $=2(4+1)$

                                        $=2(5)$

                                        $=10units$

hence,the length , breath,and perimeter of the rectangle are$4 units$ , $1 unit$ and $10 units$ respectively.