Question

A rectangular lawn has an area of 140 square yards. It’s length is six less than twice the width. What are the width and length of the lawn ?

Answer 1

The width is 10 and the length is 14.

Explanation:

To draw this conclusion, first use the equation A = lw = 140 .

Remember the length is six less than twice the width, in other words, the length equals 2 time the width minus 6: l = 2w - 6

Now you want to substitute numbers in:

140 = (2w - 6)(w)

140 = 2w^2 - 6w

2w^2 - 6w -140 = 0

w^2 - 3w - 70 = 0

Factorable by inspection!

(w - 10)(w + 7) = 0

w = 10

w = -7 (nonsense - ignore)

I = 14

Answer 2

Answer: Width= 10 yards

Length = 14 yards

Explanation:

Given : A rectangular lawn has an area of 140 square yards. It’s length is six less than twice the width.

Let x denotes the width of the rectangle .

Then, length = 2x-6

Formula : Area of rectangle = length x width

By considering the given question , we have

`(2x-6)* x = 140`

`\Rightarrow\ 2x^2-6x = 140`

`\Rightarrow\ 2(x^2-3x )= 2(70)`

`\Rightarrow\ x^2-3x = 7`

`\Rightarrow\ x^2-3x - 70=0`

`\Rightarrow\ x^2+7x-10x - 70=0`

`\Rightarrow\ x(x+7)-10(x + 7)=0`

`\Rightarrow\ (x+7)(x -10)=0`

`\Rightarrow\ (x+7)=0\ or \ (x -10)=0`

`\Rightarrow\ x=-7\ or\ x= 10`

But width cannot be negative.

⇒ Width = x = 10 yards

⇒ Length = 2x-6 = 2(10)-6= 20-6 = 14 yards

Hence, the width and length of the lawn are 10 yards and 14 yards.