Question

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.

Answer 1

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 = $2x-7$

Given : The area of the floor = 85 square feet

We know that the area of a rectangle is given by :-

$A=l\times w$

$\Rightarrow\ 85=(2x-7)\times x\\\\\Rightarrow\ 2x^2-7x-85=0\\\\\ x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\Rightarrow\ x=\dfrac{7\pm\sqrt{49-4(2)(-85)}}{4}\\\\\Rightarrow\ x=\dfrac{7\pm27}{4}\\\\\Rightarrow\ x=\dfrac{17}{2}, -5$

But dimension cannot be negative

So, the width of the floor = $x=\dfrac{17}{2}=8.5\text{ feet}$

And the length of the floor = $2(8.5)-7=10\text{ feet}$

Answer 2

Answer:

The width of rectangular floor shed =8.5 feet

Length of rectangular floor shed= $2\times8.5-7=10 feet$

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=$length\times breadth$

According to question

Area of rectangular floor shed=$x\times (2x-7)$

$x(2x-7)=85$

$2x^-7x-85=0$

It is a quadratic equation

Using factorization method

$2x^2-17 x+10 x-85=0$

$x(2x-17)+5 (2 x-170)=0$

$(2x-17)(x+5)=0$

$x=\frac{17}{2} =8.5 and x=-5$

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= $2\times8.5-7=10 feet$