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

length = 18 m

width = 7 m

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

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

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 * 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