Answer:
The area of a rectangle is 45 yd. The length and width of the given rectangle are 10 and 4.5 yards respectively.
Solution:
The area of the rectangle is given as 45 yard
The relation given to us is the length of the rectangle is 1 yd more than twice the width.
Let length and width be denoted as l and b respectively.
Now as per the given relation we have;
L = 1 + 2b ---- eq 1
We know the area of the rectangle is
Area of rectangle= l × b = 45 --eq 2
From eq 1 and eq 2 we can calculate the dimensions of the rectangle.
[tex]\text { Let } l=\frac{45}{b} \text { from eq } 1[/tex]
Substituting in eq 2 we get,
[tex]\frac{45}{b}=1+2 b[/tex]
On solving we get,
[tex]2 b^{2}+b-45=0[/tex]
On solving the quadratic equation we get
Width = 4.5 or -5.
Since length cannot be negative, the width of the rectangle is 4.5 yards.
So the length of the rectangle becomes:
l × 4.5 = 45
l = 10
The length and width of the given rectangle are 10 and 4.5 yards respectively.
