Question

The dimensions, in centimetres, of this rectangle are shown as algebraic expressions.
Not to scale
5x-y-8
3x + y-4
2x-6-3
3x + 5y +4
Work out the length and width of the rectangle.

Answer 1

Answer:

length = 15

Width = 9

Step-by-step explanation:

In a rectangle opposite sides are equal.

5x - y- 8 =3x +5y + 4

5x - 3x  -y - 5y = 4 + 8

2x - 6y = 12

Divide the entire equation by 2

x  - 3y = 6  --------------(I)

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

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

x + 7y = 1 -------------(II)

Multiply equation (II) by (-1)

(I)            x - 3y = 6

(II)*(-1)    -x - 7y = -1   {Now add. 'x' will be eliminated}

                  -10y= 5

                      y = 5/(-10)

                     y = -0.5

Plugin y = -0.5 in equation (I)

x - 3*(-0.5) = 6

x  + 1.5 = 6

        x = 6 - 1.5

        x = 4.5

Length = 5x - y - 8

           = 5*4.5 - (-0.5) - 8

           = 22.5 + 0.5 - 8

            = 23 - 8

Length = 15

Width = 2x - 6y - 3

         = 2*4.5 - 6*(-0.5) - 3

         =  9 + 3 - 3

Width = 9