Respuesta :
Length of the rectangle is 51 inches
Solution:
Given that
Length of the rectangle in 34 miles less than 5 times its width
Area of rectangle = 867 square inches
Need to determine length of the rectangle.
Let assume width of the rectangle be represented by variable x.
So 5 times width of the rectangle =5x
34 inches less than 5 times width of the rectangle = 5x – 34
As Length of the rectangle in 34 miles less than 5 times its width
=> Length of the rectangle = 5x – 34
The formula for rectangle is given as:
[tex]\text { area of rectangle }=length \times width[/tex]
As given that Area of rectangle = 867 square inches
[tex]\begin{array}{l}{=>867=(5 x-34) \times(x)} \\\\ {=>5 x^{2}-34 x-867=0}\end{array}[/tex]
On solving quadratic equation by using quadratic formula
[tex]x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}[/tex]
In our case a = 5, b = -34 and c = -867
On substituting value of a, b and c in quadratic formula we get
[tex]\begin{array}{l}{x=\frac{-(-34) \pm \sqrt{(-34)^{2}-4 \times 5 \times(-867)}}{2 \times 5}} \\\\ {=>x=\frac{34 \pm \sqrt{18496}}{10}=\frac{34+136}{10}} \\\\ {=>x=\frac{34+136}{10}=17 \text { or } x=\frac{34-136}{10}=-10.2}\end{array}[/tex]
Since x represents width, it cannot be negative, so x = 17
Length of the rectangle = 5x – 34 = 5(17) – 34 = 51
Hence length of the rectangle is 51 inches
