Respuesta :
Let the length of the rectangle to be a value, x.
Since you are told that the length is 4 feet shorter than width, then, this can only mean that
width = (x+4)
The area of a rectangle = length × width.
= x(x+4) = 42
=x² + 4x=42
From here form the quadratic equation then solve it to get the value of x (length of the rectangle)
x²+4x-42=0
Using the quadratic formula,
x = -4 + or - (√(16-4×1×-42))÷2
At this point I had a problem with inserting an equation in this platform. So, i have done it have attached a file that explains the above statement. Kindly find it in the attachment below.
x = (-4+or - 13.56)÷2
= 9.56÷2
=4.78 feet
The length to the nearest foot = 5 feet.
The width to the nearest foot = 5+4 = 9 feet.
Since you are told that the length is 4 feet shorter than width, then, this can only mean that
width = (x+4)
The area of a rectangle = length × width.
= x(x+4) = 42
=x² + 4x=42
From here form the quadratic equation then solve it to get the value of x (length of the rectangle)
x²+4x-42=0
Using the quadratic formula,
x = -4 + or - (√(16-4×1×-42))÷2
At this point I had a problem with inserting an equation in this platform. So, i have done it have attached a file that explains the above statement. Kindly find it in the attachment below.
x = (-4+or - 13.56)÷2
= 9.56÷2
=4.78 feet
The length to the nearest foot = 5 feet.
The width to the nearest foot = 5+4 = 9 feet.
Length is [tex]\boldsymbol{4.4}[/tex] feets and width is equal to [tex]\boldsymbol{8.8}[/tex] feets.
Area of a rectangle
The area of a two-dimensional region, form, or planar lamina in the plane is the quantity that expresses its extent.
A quadrilateral having four right angles is known as a rectangle.
Let [tex]\boldsymbol{w}[/tex] feets denotes width of a rectangle.
Length of a rectangle [tex]=\boldsymbol{w-4}[/tex] feets
Area of a rectangle [tex]=\boldsymbol{42}[/tex] square feet
Length [tex]\times[/tex] Width [tex]=42[/tex]
[tex]w(w-4)=42[/tex]
[tex]w^2-4w-42=0[/tex]
[tex]w=\frac{4\pm \sqrt{16+168}}{2}[/tex]
[tex]=2\pm \sqrt{46}[/tex]
As dimension can not be negative, [tex]2-\sqrt{46}[/tex] is rejected.
So,
[tex]w=2+ \sqrt{46}[/tex]
[tex]=\boldsymbol{8.8}[/tex] feets
Length [tex]=8.8-4[/tex]
[tex]=\boldsymbol{4.4}[/tex] feets
So, length is [tex]4.4[/tex] feets and width is equal to [tex]8.8[/tex] feets.
Find out more information about rectangle here:
https://brainly.com/question/10046743?referrer=searchResults
