the perimeter of a rectangle is 24cm. if x is equivalent to its length, find its possible dimension if the area of the same rectangle is less than 35sq. cm
What are the factors of 35?
1 * 35 makes p=72
5 * 7 makes p=24
But, you said the area is less than 35, so the rectangle must be less square.
So, pick any small amount near x=5, and adjust the length
4.9 * 7.1 = 34.79, and p is still 24
Secret
To find the dimensions of the rectangle, you need to set up equations based on the given information. Let's denote the length of the rectangle as x and the width as y.
The perimeter of a rectangle is given by the formula: 2(x + y) = 24cm.
Simplifying the equation, we get: x + y = 12cm.
The area of a rectangle is given by the formula: A = x * y.
Since we're looking for a rectangle with an area less than 35 square cm, the inequality becomes: A < 35.
Substituting x * y for A, the inequality becomes: x * y < 35.
Now, we have a system of equations:
1) x + y = 12cm
2) x * y < 35
To find the possible dimensions, we can use a trial and error approach by substituting different values for x and finding the corresponding y that satisfies the conditions.
Let's start by assuming x = 4cm:
Plugging this value into equation 1, we get: 4 + y = 12.
Solving this equation, we get: y = 8cm.
Now, let's calculate the area using x = 4cm and y = 8cm:
A = 4 * 8 = 32 square cm.
Since this area (32 square cm) is less than 35 square cm, it is a valid solution.
Therefore, one possible dimension for the rectangle could be x = 4cm and y = 8cm.