Question

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?

Answer 1

The length of the rectangle = 12 feet

The width of the rectangle = 5 feet

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 answer:-

The length of the rectangle = 12 feet

The width of the rectangle = 5 feet