Question

A rectangle has a length that is 5 inches greater than its width the equation is (x+5)x=104 x is the width what is the width and length of the rectangle

Answer 1

Width 8 inches

Length 13 inches.

Explanation:

We have been given that a rectangle has a length that is 5 inches greater than its width and its area is 104 square inches. The equation
`(x+5)x=104` represents the situation, where x represents the width of the rectangle.

Let us solve for x to find the width of the rectangle.

Using distributive property, we will get:

`x^2+5x=104`

`x^2+5x-104=104-104`

`x^2+5x-104=0`

Now we will split the middle term as:

`x^2+13x-8x-104=0`

`x(x+13)-8(x+13)=0`

`(x+13)(x-8)=0`

Using zero product property, we will get:

`x+13=0, x-8=0`

`x=-13, x=8`

Since width cannot be negative, therefore, the width of the rectangle is 8 inches.

Length of the rectangle would be
`x+5\Rightarrow 8+5=13`

Therefore, the length of the rectangle is 13 inches.