Answer:
Width 8 inches
Length 13 inches.
Step-by-step 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 [tex](x+5)x=104[/tex] 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:
[tex]x^2+5x=104[/tex]
[tex]x^2+5x-104=104-104[/tex]
[tex]x^2+5x-104=0[/tex]
Now we will split the middle term as:
[tex]x^2+13x-8x-104=0[/tex]
[tex]x(x+13)-8(x+13)=0[/tex]
[tex](x+13)(x-8)=0[/tex]
Using zero product property, we will get:
[tex]x+13=0, x-8=0[/tex]
[tex]x=-13, x=8[/tex]
Since width cannot be negative, therefore, the width of the rectangle is 8 inches.
Length of the rectangle would be [tex]x+5\Rightarrow 8+5=13[/tex]
Therefore, the length of the rectangle is 13 inches.
