A rectangle has a length of 17 inches less than 7 times its width. If the area of the rectangle is 2204 square inches, find the length of the rectangle.

Question

 quadratic equation question

Answer 1

Let the width of rectangle is "b" and length is "l"
It is given that length of rectangle is 17 inches less than 7 times of its width

l= 7b-17

area of rectangle is;

area= length * width

2204=(7b-17)*b

7b²-17b=2204
7b²-17b-2204=0
this is a quadratic equation

to solve this, you just multiply 2204 with 7 then split the value into two in such a way that theor sum is equivalent to -17 and product is -15428

 

7b²-17b-2204=0

7b²-133b+116b-2204=0

7b(b-19)+116(b-19)=0

(b-19) (7b+116)=0

 

so, 

b-19=0

b=19

 

7b+116=0

b=-116/7

 

so the width or length of rectangle can not be a negative value so width of that rectangle is 19 inches

length of rectangle, l=7b-17

 

=7*19 -17

=133-17

=116 inches 

 

you can check it by putting the values of width and length into formula of area of rectangle

 

area= b*l

      = 19*116 square inches

      = 2204 square inches