Question : The perimeters of two similar triangles are 36 cm and 24 cm, respectively. Find the ratio of their areas.
Option 1: 6 : 13
Option 2: 2 : 3
Option 3: 9 : 4
Option 4: 35 : 24
Correct Answer: 9 : 4
Solution : The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. In this case, the corresponding sides are in the ratio of the perimeters. So, the ratio of the areas of the two triangles is: $\left(\frac{36}{24}\right)^2 = \left(\frac{3}{2}\right)^2 = \frac{9}{4}=9:4$ Hence, the correct answer is 9 : 4.
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Question : The areas of the two triangles are in the ratio 4 : 3 and their heights are in the ratio 6 : 5. Find the ratio of their bases.
Option 1: 5 : 6
Option 2: 10 : 9
Option 3: 6 : 5
Option 4: 9 : 10
Question : The areas of two similar triangles ABC and PQR are 64 cm2 and 144 cm2, respectively. If the greatest side of the smaller ΔABC is 24 cm, then what is the greatest side of the bigger ΔPQR?
Option 1: 32 cm
Option 2: 24 cm
Option 3: 42 cm
Option 4: 36 cm
Question : The perimeter of two similar triangles is 30 cm and 20 cm, respectively. If one side of the first triangle is 9 cm. Determine the corresponding side of the second triangle.
Option 1: 13.5 cm
Option 2: 6 cm
Option 3: 15 cm
Option 4: 5 cm
Question : Two isosceles triangles have equal vertical angles and their areas are in the ratio 9 :16. Then the ratio of their corresponding heights is:
Option 1: 4.5 : 8
Option 2: 4 : 3
Option 3: 8 : 4.5
Option 4: 3 : 4
Question : If the radius of two circles is 6 cm and 9 cm and the length of the transverse common tangent is 20 cm, then find the distance between the two centres.
Option 1: 25 cm
Option 2: 22 cm
Option 3: 24 cm
Option 4: 27 cm
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