Answer: Length = 10 feet and width = 8.5 feet.
Step-by-step explanation:
Let x be the width of the floor.
Then length of the floor = [tex]2x-7[/tex]
Given : The area of the floor = 85 square feet
We know that the area of a rectangle is given by :-
[tex]A=l\times w[/tex]
[tex]\Rightarrow\ 85=(2x-7)\times x\\\\\Rightarrow\ 2x^2-7x-85=0\\\\\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\Rightarrow\ x=\dfrac{7\pm\sqrt{49-4(2)(-85)}}{4}\\\\\Rightarrow\ x=\dfrac{7\pm27}{4}\\\\\Rightarrow\ x=\dfrac{17}{2}, -5[/tex]
But dimension cannot be negative
So, the width of the floor = [tex]x=\dfrac{17}{2}=8.5\text{ feet}[/tex]
And the length of the floor = [tex]2(8.5)-7=10\text{ feet}[/tex]
Answer:
The width of rectangular floor shed =8.5 feet
Length of rectangular floor shed= [tex]2\times8.5-7=10 feet [/tex]
Step-by-step explanation:
We are given that a floor is in rectangular shape.
We have to find the length and width of rectangular floor shed.
The area of floor shed=85 square feet
Let width of floor shed=x feet
Length of floor shed=(2 x-7 ) feet
Area of rectangle=[tex]length\times breadth[/tex]
According to question
Area of rectangular floor shed=[tex] x\times (2x-7)[/tex]
[tex]x(2x-7)=85[/tex]
[tex]2x^-7x-85=0[/tex]
It is a quadratic equation
Using factorization method
[tex] 2x^2-17 x+10 x-85=0[/tex]
[tex] x(2x-17)+5 (2 x-170)=0[/tex]
[tex](2x-17)(x+5)=0[/tex]
[tex]x=\frac{17}{2} =8.5 and x=-5[/tex]
x=-5 is not possible because length and breadth of rectangle are always a natural number .
Therefore, the width of rectangular floor shed =8.5 feet
Length of rectangular floor shed= [tex]2\times8.5-7=10 feet [/tex]
