The length of the rectangle is 43 yards.
The width of the rectangle is 10 yards.
Explanation:
It is given that the perimeter of the rectangle is 106 yards.
Let [tex]l=3+4w[/tex] where l is the length of the rectangle and
w is the width of the rectangle.
The formula for the perimeter of the rectangle is given by
[tex]P=2l+2w[/tex]
Substituting the values of P and l, we have,
[tex]106=2(3+4w)+2w[/tex]
Simplifying, we have,
[tex]106=6+8w+2w[/tex]
Subtracting both sides by 6, we have,
[tex]100=10w[/tex]
Dividing by 10, we get,
[tex]10=w[/tex]
Thus, the width of the rectangle is 10 yards.
Now, substituting [tex]10=w[/tex] in [tex]l=3+4w[/tex], we get,
[tex]l=3+4(10)\\l=3+40\\l=43[/tex]
Thus, the length of the rectangle is 43 yards.
Hence, the length and breadth of the rectangle are 43 yards and 10 yards respectively.
