The length of a rectangle is given by (x+9) feet and the width is (x+2) feet. If the area is 60 square feet, what are the length and width?

The length of the rectangle  = 12 feet

The width of the rectangle  = 5 feet

Step-by-step explanation:

Step(i):-

Given that the length of the rectangle = (x+9)feet

Given that the width of the rectangle = (x+2)feet

Area of the rectangle = 60 square feet ...(i)

we know that

Area of the rectangle = length × width

                                     = (x+9)(x+2) (ii)

Equating (i) and (ii) , we get

                   (x+9)(x+2) = 60

            ⇒ x² + 2x +9 x +18 =60

            ⇒ x² +11 x +18-60 =0

          ⇒  x² + 11 x -42 =0

          ⇒ x² +14 x -3 x - 42 =0

        ⇒  x (x+14) -3(x+14) =0

          ⇒ (x -3) ( x+14) =0

        ⇒  x -3 =0 and x+14 =0

     ⇒   x=3 and x=-14

step(ii):-

we choose value x =3

The length of the rectangle = (3+9) = 12 feet

The width of the rectangle = (3+2) = 5 feet

Final -

The length of the rectangle  = 12 feet

The width of the rectangle  = 5 feet

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

mark brainliest!