a The given information is enough to find the length of the unknown sides.
B
b The scale factor is 5, which means the sides of the actual doll house should be 5 times as long.
C
c Divide the perimeter of the actual doll house by the perimeter of the drawings.
D
d Divide the area of the actual doll house with the area of the drawings.
A
aPerimeter: 70 cm
Area: 192 cm^2
B
bPerimeter: 350 cm
Area: 4800 cm^2 Drawing:
C
cRatio: 5
Explanation: See solution.
D
dRatio: 25
Explanation: See solution.
Practice makes perfect
a Using the measurements from the floor plan, we can identify all the unknown sides.
When we know all sides, we can calculate the perimeter by adding them.
12+20+9+8+3+4+6+8=70 cm
To find the area we will divide the floor plan into three different rectangles.
To calculate the rectangles' area we need their width and length. From the diagram, we see that we have all of these dimensions and we can find the floor plan's area by adding these products.
(6)( 20)+ (8)(6)+ (3)(8)=192 cm^2
b To find the sides of the actual dollhouse we have to multiply all measurements in the drawing by 5.
3 (5 )&= 15 cm
4 (5 )&= 20 cm
6 (5 )&= 30 cm
8 (5 )&= 40 cm
9 (5 )&= 45 cm
12 ( 5) &= 60 cm
20 ( 5) &= 100 cm
Now we can draw a similar figure and label the sides with the actual measurements.
Like in Part A, we have all the necessary information to find the area and perimeter of the shape.
60+100+45+40(2)+15+20+30&=350cm
(30)( 100)+ (40)(30)+ (15)(40)&=4800cm^2
c From Part A and Part B, we know that the perimeter of the drawing is 70 cm and the perimeter of the actual doll house is 350 cm. With this information, we can find the quotient of the perimeters.
350/70=5
As we can see, the quotient of the actual doll house and the drawing equals the scale factor.
d From Part A and Part B we know that the area of the drawing is 192cm^2 and the area of the actual doll house is 4800 cm^2. With this information we can find the quotient of the areas.
4800/192=25
The quotient of the actual doll house and the drawing equals the scale factor squared.
