Given:
The length of a rectangle is one unit more than its width.
Area of rectangle = 56 units
To find:
The dimensions of the rectangle.
Solution:
Let, width of the rectangle be x.
Then, length of the rectangle = x+1
Area of a rectangle is
[tex]Area=length\times width[/tex]
[tex]56=(x+1)\times x[/tex]
[tex]56=x^2+x[/tex]
[tex]0=x^2+x-56[/tex]
By splitting the middle term, we get
[tex]x^2+8x-7x-56=0[/tex]
[tex]x(x+8)-7(x+8)=0[/tex]
[tex](x-7)(x+8)=0[/tex]
Using zero product property, we get
[tex]x-7=0[/tex] and [tex]x+8=0[/tex]
[tex]x=7[/tex] and [tex]x=-8[/tex]
Width cannot be negative. So, x=7.
Now,
Width = 7 units
Length = 7+1
= 8 units
Therefore, the length of the rectangle is 8 units and width is 7 units.
