Question

Area of the rectangle is 126 sqaure meters. Length of the rectangle is 4 more than 2 times its width. Find length and width of the rectangle​

Answer 1

Answer:

       length = 18 m

       width  = 7 m

Step-by-step explanation:

Finding the length and width of rectangle

       Let the width of the rectangle = w m

                                            Length = ( 2w + 4) m

Area of rectangle = 126 square meters

length * width     = 126

 (2w + 4) * w        = 126

     2w² + 4w       = 126

     2w² + 4w - 126 = 0

Divide the entire equation by 2

        w² + 2w - 63  = 0

        Sum  = 2

    Product = -63

   Factors  =  9 , (-7)        { 9 +(-7) = 2  & 9*(-7) = -63}

w² +  9w - 7w - 63 = 0       {rewrite the middle term using the factors}

w( w + 9) - 7(w + 9) =0

        (w +9)(w - 7)  = 0

{Ignore w +9 = 0, as measurement will not come in negative}

w - 7 = 0

       w = 7

length = 2w + 4

           = 2*7 + 4

           = 14 + 4

            = 18

length = 18 m

 width = 7 m

Answer 2

Answer:

• Length of the rectangle = 18 m
• Width of the rectangle = 7 m

Step-by-step explanation:

Given:

• Area of the Rectangle = 126 m²
• Length of the rectangle is 4 more than 2 times its width.

To Find:

• Length and width

Solution:

Let's assume :

• Width of the rectangle = x
• Length of the recangle = 2x + 4

We know that,

$\: \: \dashrightarrow\sf \: \: \: Length \times Width = Area_{(Rectangle)}$

On Substituting the required values, we get:

$\\ \: \: \dashrightarrow\sf \: \: \:(2x+ 4)(x) = 126 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2 {x}^{2} + 4x = 126 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2 {x}^{2} + 4x - 126 =0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:2( {x}^{2} + 2x - 63) = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: {x}^{2} + 2x - 63 = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: {x}^{2} - 7x + 9x - 63 = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:x(x - 7) + 9(x - 7) \\ \\ \\ \: \: \dashrightarrow\sf \: \: \:(x - 7)(x + 9) = 0 \\ \\ \\ \: \: \dashrightarrow\sf \: \: \: \purple {x = 7 \: or \: - 9}$

Length of the side of the rectangle can't be negative. So, x = 7

Hence,

• Width of the rectangle = x = 7 m
• Length of the rectangle = 2x + 4 = 2(7) + 4 = 18 m