A rectangle has a length of 5 cm and a width of 4 cm. Every dimension is
tripled to form a second rectangle.
What is the ratio of the areas of the two
rectangles?

1:9

Step-by-step explanation:

First Rectangle:

width x height = area

4 * 5 = 20

Second Rectangle:

(4*3)*(5*3)=x

12 * 15 = 180

Ratio:

180/20 = 90

1:9

1:9 or 1/9

Step-by-step explanation:

if a rectangle is 5cm × 4cm

Area of rectangle= length ×width

= 5 × 4

=20cm²

if we triple dimensions of a rectangle we get the second rectangle

therefore, (5×3)cm × (4×3)cm

Area of second rectangle= 12 ×15

=180cm²

ratio is 20/180= 1/9 (Ans.)

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.