Answer:
The width is 10 and the length is 14.
Step-by-step 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: 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
[tex](2x-6)\times x = 140[/tex]
[tex]\Rightarrow\ 2x^2-6x = 140[/tex]
[tex]\Rightarrow\ 2(x^2-3x )= 2(70)[/tex]
[tex]\Rightarrow\ x^2-3x = 7[/tex]
[tex]\Rightarrow\ x^2-3x - 70=0[/tex]
[tex]\Rightarrow\ x^2+7x-10x - 70=0[/tex]
[tex]\Rightarrow\ x(x+7)-10(x + 7)=0[/tex]
[tex]\Rightarrow\ (x+7)(x -10)=0[/tex]
[tex]\Rightarrow\ (x+7)=0\ or \ (x -10)=0[/tex]
[tex]\Rightarrow\ x=-7\ or\ x= 10[/tex]
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.
