Arectangular lawn has an area of 140 square yards.

Ответ:

tammydbrooks43

07.01.2022

Width= 10 yards

Length = 14 yards

Step-by-step 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

$(2x-6)\times x = 140$

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

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

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

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

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

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

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

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

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

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.

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