Answer:
The width of rectangle is 1 unit.
Step-by-step explanation:
Given:
The area of rectangle is 6 units and its width is 5 units less than the length.
So, to find the width of rectangle.
Let the length be [tex]x[/tex] and the width be [tex]x-5[/tex].
Now, to find the width we put the formula of area of rectangle:
Area = length × width
[tex]6= x\times (x-5)[/tex]
[tex]6=x^{2}-5x[/tex]
[tex]0=x^{2}-5x-6[/tex]
[tex]0=x^{2}-6x+x-6[/tex]
[tex]0=x(x-6)+1(x-6)[/tex]
[tex]0=(x-6)(x+1)[/tex]
On solving equation we get:
[tex]x-6=0, x+1=0[/tex]
Therefore, we take the value x=6 as it is positive value:
[tex]x-6=0[/tex]
[tex]x=6[/tex]
So, the width of rectangle:
Width = [tex]x-5[/tex]
= [tex]6-5[/tex]
= [tex]1[/tex]
Therefore, the width of rectangle is 1 unit.
