Use the formulas for the area and perimeter of a rectangle to solve this problem.
Draw a rectangle that has:
an area of 35 square centimeters
a perimeter of 24 centimeters
The point on the grid represents one vertex of this rectangle.
Draw the sides of the rectangle along the grid lines. Each square in the grid has a side length of 1 centimeter.
Let the length of the rectangle be "l" and the width of the rectangle be "w".
We know that the area of a rectangle is given by the formula A = l * w and the perimeter of a rectangle is given by P = 2(l + w).
Given that the area of the rectangle is 35 square centimeters, we have:
35 = l * w
Given that the perimeter of the rectangle is 24 centimeters, we have:
24 = 2(l + w)
Solving the first equation for one of the variables, we get:
l = 35 / w
Substitute this into the second equation:
24 = 2(35 / w + w)
24 = 70 / w + 2w
Multiplying by w to get rid of the denominator:
24w = 70 + 2w^2
2w^2 - 24w + 70 = 0
Solving this quadratic equation, we get two possible solutions for w: w = 5 or w = 7.
If w = 5, then l = 35 / 5 = 7. Thus, the rectangle would have dimensions of 7 cm by 5 cm.
If w = 7, then l = 35 / 7 = 5. Thus, the rectangle would have dimensions of 5 cm by 7 cm.
Therefore, there are two possible rectangles that satisfy the given conditions.