Answer:
-The area of the second enlargement is 1,944 square inches
-The area of the second enlargement is (3 squared) squared times the original area.
-The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor
Step-by-step explanation:
<u><em>The complete question is</em></u>
Miranda enlarged a picture twice as shown below, each time using a scale factor of 3.
A rectangle with length 6 inches and width 4 inches is enlarged twice.
Which statements apply to the enlargements? Select three options.
-The area of the first enlargement is 72 square inches.
-The area of the second enlargement is 1,944 square inches.
-The area of the second enlargement is (3 squared) squared times the original area.
-The area of the second enlargement is 3 times the area of the first enlargement.
-The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor.
<u>Verify each statement</u>
1) The area of the first enlargement is 72 square inches.
The statement is false
Because
we know that
The original dimensions of the rectangle are
length 6 inches and width 4 inches
so
<em>First enlargement</em>
Multiply the original dimensions by a scale factor of 3
The area of the first enlargement is
2) The area of the second enlargement is 1,944 square inches
The statement is true
Multiply the dimensions of the first enlargement by a scale factor of 3
The area of the second enlargement is
3) The area of the second enlargement is (3 squared) squared times the original area.
The statement is true
Because
The original area is
The area of the second enlargement is
so
4) The area of the second enlargement is 3 times the area of the first enlargement
The statement is false
Because
so
5) The ratio of the area of the first enlargement to the area of the original equals the square of the scale factor
The statement is true
Because
The square of the scale factor is 3^2=9
and the ratio is equal to