A rectangle measuring 7cm by 4cm is enlarged by ratio 2:1?
a)what's area
1)the original reactangle
2)the enlarged rectangle
b)by what ratio has the area been enlarged
original rectangle:
area = 7(4) cm^2 = 28 cm^2
new rectangle:
area = (14)(8) cm^2 = 112 cm^2
ratio of new to old = 112 : 28 = 4 : 1
The ratio of the areas of similar figures is proportional to the square of their corresponding sides, that is
2^2 : 1^2
= 4 : 1
a)
1) The original rectangle's area is 7 cm * 4 cm = 28 square cm.
2) The enlarged rectangle's dimensions are (2 * 7) cm by (2 * 4) cm, which is 14 cm by 8 cm. So the area of the enlarged rectangle is 14 cm * 8 cm = 112 square cm.
b) The area has been enlarged by a ratio of 112 square cm : 28 square cm, which simplifies to 4:1. So, the area has been enlarged by a ratio of 4:1.
To find the areas of the rectangle, we can multiply the length and width of each rectangle.
a)
1) The original rectangle:
Area = length * width
= 7 cm * 4 cm
= 28 cm^2
2) The enlarged rectangle:
The ratio of enlargement is 2:1. Let's call the new dimensions of the enlarged rectangle L' and W'.
L' = 2 * 7 cm
= 14 cm
W' = 2 * 4 cm
= 8 cm
Area = L' * W'
= 14 cm * 8 cm
= 112 cm^2
b)
To find out by what ratio the area has been enlarged, we can divide the area of the enlarged rectangle by the area of the original rectangle:
Ratio = (Area of the enlarged rectangle) / (Area of the original rectangle)
= 112 cm^2 / 28 cm^2
= 4:1
Therefore, the area has been enlarged by a ratio of 4:1.
To find the area of a rectangle, you multiply its length (L) by its width (W).
a) To determine the areas:
1) For the original rectangle with dimensions 7cm by 4cm, the area is calculated as follows: Area = length x width = 7cm x 4cm = 28 square cm.
2) For the enlarged rectangle, you need to apply the given ratio of 2:1 to both the length and width. Since the ratio is 2:1, this means that the new length will be 2 times the original length, and the new width will be 1 time the original width. Let's calculate the new length and width before calculating the area:
New length = 2 x 7cm = 14cm
New width = 1 x 4cm = 4cm
Now, we can calculate the area of the enlarged rectangle: Area = length x width = 14cm x 4cm = 56 square cm.
b) To determine the ratio by which the area has been enlarged, you need to compare the areas of the original and enlarged rectangles.
Ratio = (Area of enlarged rectangle) / (Area of original rectangle)
Ratio = 56 square cm / 28 square cm = 2:1
So, the area of the original rectangle is 28 square cm, the area of the enlarged rectangle is 56 square cm, and the area has been enlarged by a ratio of 2:1.