The scale drawing of a swimming pool measures 2 inches by 3 inches. On the drawing .25 inches = 3 feet. What are the actual dimensions of the pool?
Responses
A 14 feet x 24 feet
B 18 feet x 24 feet
C 24 feet x 36 feet
D 30 feet x 40 feet
E 35 feet x 45 feet
C 24 feet x 36 feet
To find the actual dimensions of the pool, we first convert the given measurements on the scale drawing to actual measurements.
Given: 2 inches x 3 inches
On the scale drawing, 0.25 inches = 3 feet
Converting the width:
2 inches x 0.25 inches per 3 feet = 0.5 inches
0.5 inches x 3 feet = 1.5 feet
Converting the length:
3 inches x 0.25 inches per 3 feet = 0.75 inches
0.75 inches x 3 feet = 2.25 feet
Therefore, the actual dimensions of the pool are 1.5 feet x 2.25 feet.
Converting to feet:
1.5 feet x 4 = 6 feet
2.25 feet x 4 = 9 feet
So, the actual dimensions of the pool are 6 feet x 9 feet.
After the scale factor is applied to the dimensions of the rectangle shown, choose all that correctly give the new dimension.
Responses
A New width after a scale factor of 3. 12 cmNew width after a scale factor of 3. 12 cm
B New length after a scale factor of 4. 80 cmNew length after a scale factor of 4. 80 cm
C New perimeter after a scale factor of 2. 112 cmNew perimeter after a scale factor of 2. 112 cm
D New area after a scale factor of 2. 160 cm/2
A New width after a scale factor of 3. 12 cm
B New length after a scale factor of 4. 80 cm
When a scale factor is applied to a shape, to find the new dimensions:
A) Width:
Original width x Scale factor
= 4 cm x 3
= 12 cm
B) Length:
Original length x Scale factor
= 20 cm x 4
= 80 cm
C) New perimeter after a scale factor of 2:
Original perimeter x Scale factor
= (2 x (width + length)) x 2
= (2 x (4 cm + 20 cm)) x 2
= 48 cm x 2
= 96 cm
None of the given options correctly states the new perimeter of 96 cm.
D) New area after a scale factor of 2:
Original area x Scale factor squared
= (4 cm x 20 cm) x (2^2)
= 80 cm^2 x 4
= 320 cm^2
There is no option provided that correctly states the new area of 320 cm^2.
C) New perimeter after a scale factor of 2:
Original perimeter x Scale factor
= (2 x (width + length)) x 2
= (2 x (4 cm + 20 cm)) x 2
= 48 cm x 2
= 96 cm
I apologize for the oversight. Thank you for pointing it out.
C) New perimeter after a scale factor of 2:
Original perimeter x Scale factor
= (2 x (width + length)) x 2
= (2 x (4 cm + 20 cm)) x 2
= (2 x 24 cm) x 2
= 48 cm x 2
= 96 cm
Therefore, the correct statement provided is:
C) New perimeter after a scale factor of 2: 96 cm