Question

Select the correct answer from each drop-down menu.

The length of a rectangle is 5 inches more than its width. The area of the rectangle is 50 square inches.
The quadratic equation that represents this situation is
The length of the rectangle is
inches.

Answer 1

Part 1) The quadratic equation is
`x^(2)-5x-50=0`

Part 2) The length of rectangle is 10 in and the width is 5 in

Explanation:

Part 1)

Find the quadratic equation

Let

x -----> the length of rectangle

y ----> the width of rectangle

we know that

The area of rectangle is equal to

`A=xy`

`A=50\ in^(2)`

so

`50=xy` -----> equation A

`x=y+5`

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

substitute equation B in equation A

`50=x(x-5)\\50=x^(2) -5x\\ x^(2)-5x-50=0`

Part 2) Find the length of the rectangle

`x^(2)-5x-50=0`

Solve the quadratic equation by graphing

The solution is
`x=10\ in`

see the attached figure

Find the value of y

`y=10-5=5\ in`

therefore

The length of rectangle is 10 in and the width is 5 in

Answer 2

Quadratic equation:
`x^(2) +5x-50=0`

Length of the rectangle: 10 inches.

Explanation:

In order to solve this you just have to factorize the equation to solve the different values for X:

`x^(2) +5x-50=0\\(x+10)(x-5)=0`

So the only possible answer for the problem would be 5, so if the width is equal to X and the length is x+5 then the length of the rectangle would be 5+5 and that would be 10.