Respuesta :
Answer:
( 7-x ) meter.
Step-by-step explanation:
Rectangle has an area of [tex](49-x^{2})meter^{2}[/tex] and width of the rectangle is given as ( 7 + x).
We have to find expression that represents length of the rectangle.
Since area of rectangle = Length × width
[tex](49-x^{2} )=(7+x)[/tex] × length
[tex](7-x)(7+x)=(7+x)[/tex] × length
[Since [tex]a^{2}- b^{2}=(a+b)(a-b)][/tex]
Length = [tex]\frac{(7-x)(7+x)}{(7+x)}[/tex]
= (7-x) meter
The expression (7-x) represents the length of the rectangle if the rectangle below has an area of (49-x^2) square meters and a width of (7+x).
What is the area of the rectangle?
It is defined as the space occupied by the rectangle which is planner 2-dimensional geometry.
The formula for finding the area of a rectangle is given by:
Area of rectangle = length × width
We have rectangle:
The area of the rectangle = (49 - x²) square meters
The width of the rectangle = (7+x) meters
Let's suppose the length of the rectangle is L
From the formula:
(49 - x²) = (7+x) L
[tex]\rm L = \frac{(49-x^2)}{(7+x)}[/tex] or
[tex]\rm L = \frac{(7^2-x^2)}{(7+x)}[/tex]
We know (a²-b²) = (a+b)(a-b)
[tex]\rm L = \frac{(7+x)(7-x)}{(7+x)}\\\\\rm L = (7-x) \ \ meters[/tex]
Thus, the expression (7-x) represents the length of the rectangle if the rectangle below has an area of (49-x^2) square meters and a width of (7+x).
Learn more about the area here:
brainly.com/question/14383947
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