The lengths of two sides of a rectangle are consecutive even integers. The perimeter of the rectangle is 196cm. Find the area.
-please help, I don’t know where to start or how to approach this problem.
even integers differ by 2, right?
So, if the width is w, then the length is w+2
Now just figure the perimeter and find w:
2(w + w+2) = 196
2 (w+w+2)=196
4w+4=196
w=48
L=50
To solve this problem, let's denote the lengths of the two sides of the rectangle as x and x+2 (since they are consecutive even integers).
The perimeter of a rectangle is found by adding the lengths of all four sides. In this case, we know that the perimeter is 196 cm. Therefore, we can set up the following equation:
2(x + x+2) = 196
Let's simplify this equation step-by-step:
1. Distribute the 2 to both terms inside the parentheses:
2x + 2(x+2) = 196
2. Simplify the expression inside the parentheses:
2x + 2x + 4 = 196
3. Combine like terms:
4x + 4 = 196
4. Subtract 4 from both sides of the equation:
4x = 192
5. Divide both sides of the equation by 4 to solve for x:
x = 48
Now, we know that x = 48. To find the other side (x+2), we can substitute the value of x back into the equation:
x + 2 = 48 + 2 = 50
So, the lengths of the rectangle's sides are 48 cm and 50 cm.
To find the area of the rectangle, we simply multiply the lengths of its sides:
Area = length × width
= 48 × 50
= 2400 cm²
Therefore, the area of the rectangle is 2400 cm².
To solve this problem, let's break it down step by step.
Step 1: Understand the problem.
We are given that the lengths of two sides of a rectangle are consecutive even integers. Let's assume that the first side has a length of x, which makes the second side x+2 (since they are consecutive even integers).
Step 2: Use the given information to form an equation or equations.
The perimeter of a rectangle can be calculated by adding the lengths of all sides. In this case, we have two sides of length x and two sides of length x+2. So the perimeter equation becomes:
Perimeter = 2*x + 2*(x+2) = 196
Step 3: Simplify the equation and solve for x.
Simplifying the equation:
2x + 2x + 4 = 196
4x + 4 = 196
4x = 196 - 4
4x = 192
Solving for x:
x = 192 / 4
x = 48
Step 4: Find the length and width of the rectangle.
The length of the rectangle is x, which is 48 cm.
The width of the rectangle is x+2, which is 48+2 = 50 cm.
Step 5: Calculate the area of the rectangle.
The area of a rectangle is given by the product of its length and width. So, the area of this rectangle is:
Area = Length * Width = 48 cm * 50 cm = 2400 cm^2
Therefore, the area of the rectangle is 2400 cm^2.