Respuesta :
The width of the classroom is 10 feet, if the area of a rectangular wall in a classroom is 280 square feet and Its length is 2 feet shorter than three times its width.
Step-by-step explanation:
The given is,
Area of rectangular is 280 square feet
Length is 2 feet shorter than three times its width
Step:1
Formula for area of rectangular,
[tex]Area, A=wl[/tex]..............................(1)
Where, w - width of the rectangle
l - Length of the rectangle
From the given,
Let, x- width of the rectangle
w = x...........................................................(2)
[tex]l = 3x - 2[/tex]...................................................(3)
( Length is 2 feet shorter than three times its width )
Equation (1) becomes,
[tex]280 = (3x-2)(x)[/tex]
[tex]280 = (3x^{2} -2x)[/tex]
= [tex]3x^{2} -2x-280[/tex]
Solution of the above equation,
x = 10 feet
Step:2
Equation (2) becomes,
w = 10 feet
Equation (3) becomes,
[tex]l = 3x - 2[/tex]
[tex]l = 3(10) - 2[/tex]
[tex]l = 30-2[/tex]
l = 28 feet
Step:3
Check for solution equation (1) becomes,
280 = (28) (10)
280 = 280
Result:
The width of the classroom is 10 feet, if the area of a rectangular wall in a classroom is 280 square feet and Its length is 2 feet shorter than three times its width.
The width of the wall of the classroom is 10 feet and this can be determined by forming the quadratic equation.
Given :
The area of a rectangular wall in a classroom is 280 square feet. Its length is 2 feet shorter than three times its width.
The following steps can be used in order to determine the width of the wall of the classroom:
Step 1 - Let the length of the rectangular wall be 'l' and the width of the wall be 'w'.
Step 2 - According to the given data the area of the rectangular wall is given by:
[tex]\rm 280 = lw[/tex] --- (1)
Step 3 - Now, it is also given that the length of the wall is 2 feet shorter than three times its width that is:
l = 3w - 2
Step 4 - Substitute the value of 'l' in the equation (1).
280 = w(3w - 2)
[tex]\rm 3w^2-2w - 280=0[/tex]
Step 5 - So, (w = 10) is one of the factors of the above quadratic equation.
So, the width of the wall of the classroom is 10 feet.
For more information, refer to the link given below:
https://brainly.com/question/11897796
