The area of a rectangle is 24 cm^2. The width is two less than the length. What is the length and width of the rectangle?
Guide On Rating System
Vote
Let the length of the rectangle be x cm.
According to the given condition, the width is two less than the length, so the width is (x-2) cm.
The area of the rectangle is length multiplied by width, so we have x(x-2) = 24 cm^2.
Expanding the equation gives x^2 - 2x = 24 cm^2.
Rearranging the equation gives x^2 - 2x - 24 = 0.
Factoring the equation gives (x-6)(x+4) = 0.
Setting each factor equal to zero gives x-6 = 0 or x+4 = 0.
Solving for x gives x = 6 or x = -4.
Since length cannot be negative, we discard the solution x = -4.
Therefore, the length of the rectangle is x = 6 cm.
The width of the rectangle is (x-2) = (6-2) = 4 cm.
So the length of the rectangle is 6 cm and the width is 4 cm. Answer: \boxed{6 \text{ cm}, 4 \text{ cm}}.
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99