Question

The length of a rectangle is the width minus 5 units. The area of the rectangle is 36 units. What is the width, in units, of the rectangle

Answer 1

The width of the rectangle is
`9\ units`

Explanation:

Let

x----> the length of rectangle

y----> the width of rectangle

we know that

The area of rectangle is equal to

`A=xy`

`A=36\ units^(2)`

so

`36=xy` ------> equation A

`x=y-5` -----> equation B

substitute equation B in equation A and solve for y

`36=(y-5)y`

`y^(2)-5y-36=0`

Solve the quadratic equation by graphing

The solution is
`y=9\ units`

see the attached figure

therefore

The width of the rectangle is
`9\ units`

Answer 2

Answer: 9 units.

Explanation:

Let x be the width of the rectangle .

Then, the length would be x-5.

Area of rectangle = Length x Breadth

`=(x-5)x=x^2-5x`

Since , The area of the rectangle is 36 units.

`\Rightarrow\ x^2-5x=36\\\\\Rightarrow\ x^2-5x-36=0\\\\\Rightarrow\ x^2-9x+4x-36=0\\\\\Rigtarrow\ x(x-9)+4(x-9)=0\\\\\Rightarrow\ (x-9)(x+4)=0\\\\\Rightarrow\ x=9 , -4`

But width cannot be negative , so width = x= 9 units

Hence, the width of the rectangle = 9 units.