The area of a rectangle is given by the expression 3x^2+7x-40.
A. What is the length of the rectangle if its width is x+5?
B. If x=2cm, find the length, width and area of the rectangle?
A.
W = x + 5
A = W ∙ L
3 x² + 7 x - 40 = ( x + 5 ) ∙ L
L = ( 3 x² + 7 x - 40 ) / ( x + 5 )
L = 3 x - 8
Question B does not make sense.
When x = 2
A = 3 x² + 7 x - 40 = 3 ∙ 2² + 7∙ 2 - 40 = 3 ∙ 4 + 14 - 40 = 12 + 14 - 40 = -14
If area is negative, length or width must be negative.
It is impossible.
To find the length of the rectangle, we need to factor the given expression for the area.
A. What is the length of the rectangle if its width is x+5?
Given:
Area = 3x^2 + 7x - 40
Width = x + 5
To find the length, we need to divide the area by the width. So, divide the expression for the area by the expression for the width:
Length = (3x^2 + 7x - 40) / (x + 5)
To simplify this expression, we can factor the numerator:
Length = [(3x - 5)(x + 8)] / (x + 5)
Therefore, the length of the rectangle is (3x - 5)(x + 8) / (x + 5).
B. If x=2cm, find the length, width, and area of the rectangle?
Given:
x = 2 cm
Area = 3x^2 + 7x - 40
To find the length and width when x = 2 cm, substitute the value of x into the expressions for length and width:
Width = x + 5 = 2 + 5 = 7 cm
To find the length, substitute the value of x into the expression for length:
Length = [(3x - 5)(x + 8)] / (x + 5)
Length = [(3(2) - 5)(2 + 8)] / (2 + 5)
Length = (1)(10) / 7
Length = 10/7 cm
To find the area, substitute the value of x into the expression for the area:
Area = 3x^2 + 7x - 40
Area = 3(2)^2 + 7(2) - 40
Area = 3(4) + 14 - 40
Area = 12 + 14 - 40
Area = -14 cm^2
Therefore, the length of the rectangle is 10/7 cm, the width is 7 cm, and the area is -14 cm^2.