Answer:
The width of rectangle is 7 inches.
The length of rectangle is 10 inches.
Step-by-step explanation:
Let w represent width and l represent length of the rectangle.
We have been given that the length of a rectangle is 3 inches more than its width. We can represent this information in an equation as:
[tex]l=w+3...(1)[/tex]
We are also told that the perimeter of the rectangle is 34 inches. We know that perimeter of a rectangle is two times its width and length. We can represent this information in an equation as:
[tex]2(w+l)=34...(2)[/tex]
Upon substituting equation (1) in equation (2), we will get:
[tex]2(w+w+3)=34[/tex]
[tex]2(2w+3)=34[/tex]
Using distributive property [tex]a(b+c)=ab+ac[/tex], we will get:
[tex]2*2w+2*3=34[/tex]
[tex]4w+6=34[/tex]
[tex]4w+6-6=34-6[/tex]
[tex]4w=28[/tex]
[tex]\frac{4w}{4}=\frac{28}{4}[/tex]
[tex]w=7[/tex]
Therefore, the width of rectangle is 7 inches.
Upon substituting [tex]w=7[/tex] in equation (1), we will get:
[tex]l=w+3[/tex]
[tex]l=7+3[/tex]
[tex]l=10[/tex]
Therefore, the length of rectangle is 10 inches.
