Respuesta :
Answer:
Length of the rectangle is 15 feet and width of the rectangle is 9 feet.
Step-by-step explanation:
Given:
Area of the rectangle = 90 square feet
We need to find the length and width of the rectangle.
Solution:
Let the width of the rectangle be denoted by 'w'.
Now given:
length is nine feet less than four times it's width.
so we can say that;
length of the rectangle = [tex]4w-9[/tex]
Now we know that;
Area of the rectangle is given by length times width.
framing in equation form we get;
[tex](4w-9)w=90\\\\4w^2-9w =90\\\\4w^2-9w-90=0[/tex]
Now we will factorize so as to find the roots.
[tex]4w^2-24w+15w -90=0\\\\4w(w-6)+15(w-6)=0\\\\(4w+15)(w-6)=0[/tex]
Now substituting separately we will find 2 value of w.
[tex]4w+15 =0 \ \ \ \ Or \ \ \ \ w-6 =0\\\\4w=-15 \ \ \ \ \ Or \ \ \ \ \ w= 6\\\\w =\frac{-15}{4} \ \ \ \ \ Or \ \ \ \ \ w= 6[/tex]
Now we get 2 value of w one positive and one negative and we know that width of the rectangle can't be negative hence we will discard negative value and consider positive value.
width of the rectangle = 6 ft
Length of the rectangle = [tex]4x-9 = 4\times6 -9 = 24 -9 =15\ ft[/tex]
Hence Length of the rectangle is 15 feet and width of the rectangle is 9 feet.
