What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 2.5? (1 point)
A rectangle is shown. The length of the rectangle is labeled as 8 cm, and the width is labeled as 6 cm.
Perimeter = 38 cm, area = 89.25 cm2
Perimeter = 38 cm, area = 300 cm2
Perimeter = 70 cm, area = 89.25 cm2
Perimeter = 70 cm, area = 300 cm2
If the rectangle is enlarged using a scale factor of 2.5, the length and width will both be multiplied by 2.5.
New length = 8 cm * 2.5 = 20 cm
New width = 6 cm * 2.5 = 15 cm
The perimeter of the rectangle is given by:
Perimeter = 2*(length + width)
Perimeter = 2*(20 cm + 15 cm)
Perimeter = 2*(35 cm)
Perimeter = 70 cm
The area of the rectangle is given by:
Area = length * width
Area = 20 cm * 15 cm
Area = 300 cm²
Therefore, the correct answer is:
Perimeter = 70 cm, area = 300 cm²
Which of the following possibilities will form a triangle? (1 point)
Side = 10 cm, side = 5 cm, side = 6 cm
Side = 10 cm, side = 6 cm, side = 3 cm
Side = 11 cm, side = 5 cm, side = 6 cm
Side = 11 cm, side = 5 cm, side = 5 cm
To form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check each possibility:
1. Side = 10 cm, side = 5 cm, side = 6 cm
10 cm + 5 cm = 15 cm > 6 cm
10 cm + 6 cm = 16 cm > 5 cm
5 cm + 6 cm = 11 cm > 10 cm
The sum of the lengths of any two sides is greater than the length of the third side in this case, so it forms a triangle.
2. Side = 10 cm, side = 6 cm, side = 3 cm
10 cm + 6 cm = 16 cm > 3 cm
10 cm + 3 cm = 13 cm > 6 cm
6 cm + 3 cm = 9 cm < 10 cm
The sum of the lengths of any two sides is not greater than the length of the third side in this case, so it does not form a triangle.
3. Side = 11 cm, side = 5 cm, side = 6 cm
11 cm + 5 cm = 16 cm > 6 cm
11 cm + 6 cm = 17 cm > 5 cm
5 cm + 6 cm = 11 cm > 11 cm
The sum of the lengths of any two sides is greater than the length of the third side in this case, so it forms a triangle.
4. Side = 11 cm, side = 5 cm, side = 5 cm
11 cm + 5 cm = 16 cm > 5 cm
11 cm + 5 cm = 16 cm > 5 cm
5 cm + 5 cm = 10 cm < 11 cm
The sum of the lengths of any two sides is not greater than the length of the third side in this case, so it does not form a triangle.
Therefore, the possibilities that will form a triangle are:
Side = 10 cm, side = 5 cm, side = 6 cm
Side = 11 cm, side = 5 cm, side = 6 cm