A rectange has dimensions of 1 and 6. Another rectangle was drawn from it using a scale factor of 1.5.
A. The area of the large rectangle is how many times the area of the small rectangle?
B. The perimter of the large rectangle is how many times the perimeter of the small rectangle?
both length and width are multiplied by 1.5 so
A. 1.5 L * 1.5 B = 2.25 L B so 2.25
B. 1.5L+1.5B+1.5L+1.5B = 1.5(2L+2B) so 1.5
What about C?
Oh sorry nevermind lol
To find the answers to these questions, we need to calculate the area and perimeter of both the small rectangle and the large rectangle.
First, let's find the area of the small rectangle.
Area of a rectangle = length × width
Given that the dimensions of the small rectangle are 1 and 6, we can substitute these values into the formula.
Area of small rectangle = 1 × 6 = 6 square units
Now, let's find the area of the large rectangle, which was obtained by scaling up the dimensions of the small rectangle by a scale factor of 1.5.
To scale up the dimensions, we multiply each dimension by the scale factor.
Length of large rectangle = 1 × 1.5 = 1.5
Width of large rectangle = 6 × 1.5 = 9
Area of large rectangle = length × width = 1.5 × 9 = 13.5 square units
Now, let's move on to answering the questions:
A. The area of the large rectangle is how many times the area of the small rectangle?
To find the ratio of the areas, we divide the area of the large rectangle by the area of the small rectangle.
Area ratio = Area of large rectangle / Area of small rectangle
= 13.5 / 6
= 2.25
Therefore, the area of the large rectangle is 2.25 times the area of the small rectangle.
B. The perimeter of the large rectangle is how many times the perimeter of the small rectangle?
The perimeter of a rectangle is the sum of all its side lengths.
Perimeter of small rectangle = 2 × (length + width)
= 2 × (1 + 6)
= 2 × 7
= 14 units
Now, let's calculate the perimeter of the large rectangle using the scaled-up dimensions.
Perimeter of large rectangle = 2 × (length + width)
= 2 × (1.5 + 9)
= 2 × 10.5
= 21 units
To find the ratio of the perimeters, we divide the perimeter of the large rectangle by the perimeter of the small rectangle.
Perimeter ratio = Perimeter of large rectangle / Perimeter of small rectangle
= 21 / 14
= 1.5
Therefore, the perimeter of the large rectangle is 1.5 times the perimeter of the small rectangle.