Answer :
Answer:
Therefore,
[tex]Length=12\ cm[/tex]
[tex]Width= 7\ cm[/tex]
Step-by-step explanation:
Let the Width of rectangle be 'x' cm.
Then the length of a rectangle will be (x + 5) cm.
Area of rectangle given is 84 cm squared.
To Find:
Length = (x+5) = ?
Width = x = ?
Solution:
We have area of rectangle given as
[tex]\textrm{Area of Rectangle}=Length\times Width[/tex]
Substituting the given values we get
[tex]84=(x+5)x\\x^{2} +5x-84=0\\[/tex]
On factorizing we get
[tex]x^{2} +12x-7x-84=0\\x(x+12)-7(x+12)=0\\(x+12)(x-7)=0\\(x+12)=0\ or\ (x-7)=0\\x=-12\ or\ x=7\\\therefore x =7\ cm\ \textrm{As x cannot be negative}[/tex]
Therefore,
[tex]Length=x+5=7+5=12\ cm[/tex]
Therefore,
[tex]Length=12\ cm[/tex]
[tex]Width= 7\ cm[/tex]