Let's assume w represent the width of the rectangle.
Given that, the length of the rectangle is 3 ft more than twice the width.
So, we can write:
Length = 3 + 2w
And area = 35
So, length * width = 35
(3+2w) * w = 35
3w +2w²=35 By distribution property.
3w + 2w²-35 = 0 Subtract 35 from each sides.
2w² + 3w - 35 = 0
Next step is to solve the above equation by factoring to get the vaue of w.
To factor the above trinomial, multiply the constant -35 with the leading coefficient 2.
So, -35*2 = -70.
Next step is to breakdown -70 into two multiples so that their addition will result the coefficient of w=3.
So, -70 = -7 * 10
And addition of -7 and 10 will give 3.
So, next step is to replace 3w with -7w + 10w. Therefore,
2w² - 7w + 10w - 35 = 0
(2w² - 7w) + (10w - 35) = 0 Make the group of two terms.
w (2w - 7) + 5 (2w - 7) = 0 Take out the common factor from each group.
(2w - 7) ( w + 5) = 0 Again take out the common factor (2w-7).
So, 2w -7 =0 and w + 5 =0 Set both the factor equal to 0.
2w = 7 and w = -5
w = 7/2
So, w = 3.5 because width cannot be negative 5.
Now plug in w=3.5 in 3 + 2w to get the length.
So, length = 3 + 2(3.5)
= 3 + 7
= 10
Hence the dimension of the rectangle is 10 ft and 3.5 ft.
