Answer :
Answer:
Width of the rectangle = 17 inches
Length of the rectangle = 31 inches
Step-by-step explanation:
Let w be the width of the rectangle.
Given:
Width of the rectangle = w
Length of the rectangle = 2w - 3
Area of the rectangle [tex]=527\ inches^{2}[/tex]
Solution:
We know that the area of the rectangle.
[tex]Area\ of\ rectangle = length\times width[/tex]
[tex]w(2w-3)=527[/tex]
[tex]2w^{2}-3w-527=0[/tex]
Now, we first find the root of the above equation.
Use quadratic formula with [tex]a=2, b=-3, c=-527[/tex].
[tex]t=\frac{-b\pm \sqrt{(b)^{2}-4ac}}{2a}[/tex]
Put a, b and c value in above equation.
[tex]w=\frac{-(-3)\pm \sqrt{(-3)^{2}-4(2)(-527)}}{2(2)}[/tex]
[tex]w=\frac{3\pm \sqrt{9+8\times 527}}{4}[/tex]
[tex]w=\frac{3\pm \sqrt{9+4216}}{4}[/tex]
[tex]w=\frac{3\pm \sqrt{4225}}{4}[/tex]
[tex]w=\frac{3\pm 65}{4}[/tex]
For positive sign
[tex]w=\frac{68}{4}[/tex]
w = 17 inches
So, width of the rectangle is 17 inches.
Length of the rectangle.
[tex]Length = 2\times w-3[/tex]
[tex]Length = 2\times 17-3[/tex]
[tex]Length = 34-3[/tex]
Length = 31 inches
So, length of the rectangle is 31 inches.
Therefore, width and length of the rectangle is 17 inches and 31 inches.