The floor of a shed given on the right has an area of 85 square feet. The floor is in the shape of a rectangle whose length is 7 feet less than twice the width. Find the length and the width of the floor of the shed.
Accepted Solution
A:
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 feetWe 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 negativeSo, 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]