Online Test — Scale Drawings & Similar Figures
10 Questions • 20 min • Chapter MCQ
20:00
Question 1 of 10
easy
Two triangles have angles 45, 65, 70 and 45, 65, 70. Are they similar?
Yes, they are similar
No, they are not
Only if sides are equal
Cannot determine
Explanation: All corresponding angles are equal, so the triangles are similar by AA.
Question 2 of 10
easy
Rectangle A: 5cm x 8cm. Rectangle B: 15cm x 24cm. What is the scale factor from A to B?
2
3
4
5
Explanation: 15/5=3 and 24/8=3. Scale factor = 3.
Question 3 of 10
medium
Two similar triangles have side ratio 2:5. What is their area ratio?
2:5
4:10
4:25
2:25
Explanation: Area ratio = (side ratio)^2 = 2^2 : 5^2 = 4:25
Question 4 of 10
medium
Triangle P ~ Triangle Q. PQ=6cm, AB=18cm. Area of P = 12cm^2. Find area of Q.
36 cm^2
72 cm^2
108 cm^2
144 cm^2
Explanation: k = 18/6 = 3. Area ratio = k^2 = 9. Area Q = 12 x 9 = 108 cm^2.
Question 5 of 10
medium
A map scale is 1:100,000. Two cities are 5 cm apart on the map. What is the actual distance?
0.5 km
5 km
50 km
500 km
Explanation: 5 cm x 100,000 = 500,000 cm = 5,000 m = 5 km
Question 6 of 10
medium
Two similar pentagons have areas 36cm^2 and 81cm^2. What is the side length ratio?
2:3
3:4
4:5
6:9
Explanation: Area ratio = 81/36 = 9/4. So k^2=9/4, k=3/2. Side ratio = 2:3.
Question 7 of 10
medium
A model airplane is 1:72 scale. The real wingspan is 18m. What is the model's wingspan?
0.25 m
0.5 m
1 m
2 m
Explanation: 18 m = 1800 cm. 1800 / 72 = 25 cm = 0.25 m
Question 8 of 10
medium
Triangle sides: 3cm, 4cm, 5cm. A similar triangle has smallest side = 9cm. Find perimeter of the larger triangle.
24 cm
30 cm
36 cm
48 cm
Explanation: k = 9/3 = 3. Original perimeter = 12 cm. Larger perimeter = 12 x 3 = 36 cm.
Question 9 of 10
medium
A photo 4 x 6 inches is enlarged to 8 x 12 inches. By what factor does the area increase?
2
4
6
8
Explanation: k=2 (linear scale). Area increases by k^2=4. Or: old area=24, new area=96, ratio=4.
Question 10 of 10
hard
Two circles are similar. Small radius=2cm, large radius=6cm. Area of small = 12.56cm^2. Find area of large circle.
37.68 cm^2
75.36 cm^2
113.04 cm^2
150.72 cm^2
Explanation: k=3, area ratio=9. Area large = 12.56 x 9 = 113.04 cm^2.