The length of a rectangle is 2 inches more than its width. The area of the rectangle is 15 square inches. What are the length and width of the rectangle?
3 by 5
Why did the rectangle go to the market? Because it wanted to square things away! Now, let's solve this puzzle together. Let's call the width of the rectangle "x". Since the length is 2 inches more than the width, we can call the length "x + 2". The area of a rectangle is found by multiplying its length and width, so we have the equation: x(x + 2) = 15. Expanding this, we get x^2 + 2x = 15. Rearranging, we have x^2 + 2x - 15 = 0. Now, let's solve for x using our good old friend, the quadratic formula. Applying the formula, we find that x = 3 or x = -5. Since we're talking about lengths, we can't have a negative value, so the width is 3 inches. Therefore, the length is 3 + 2 = 5 inches. The dimensions of the rectangle are 5 inches by 3 inches. Ta-da!
Let's denote the width of the rectangle as "w" inches.
According to the problem, we know that the length is 2 inches more than the width. Therefore, we can represent the length as "w + 2" inches.
The formula for calculating the area of a rectangle is length times width. In this case, the area is given as 15 square inches. So we have the equation:
Area = Length * Width
15 = (w + 2) * w
To solve this equation, we can expand and rearrange it:
15 = w^2 + 2w
w^2 + 2w - 15 = 0
Now we need to factorize or use the quadratic formula to find the values of "w" that satisfy this equation.
Factoring, we have:
(w - 3)(w + 5) = 0
This gives us two possible solutions for "w":
w - 3 = 0 or w + 5 = 0
If we solve these equations, we find:
w = 3 or w = -5
Since the width of a rectangle cannot be negative, we discard the solution w = -5.
Therefore, the width of the rectangle is 3 inches.
We can substitute this value back into the equation for the length:
Length = Width + 2
Length = 3 + 2 = 5
So, the length of the rectangle is 5 inches.
To find the length and width of the rectangle, we can use the given information.
Let's assume the width of the rectangle as 'w' inches.
According to the problem, the length is 2 inches more than the width. So the length of the rectangle can be written as 'w + 2' inches.
To find the area of the rectangle, we can use the formula:
Area = Length * Width
Substituting the given values, we have:
15 = (w + 2) * w
Now let's solve this equation to find the width of the rectangle.