Similar figures: ratio of areas is the square of the ratio of sides (or perimeters, altitudes)
This type of question, asked 11 times: 18 Jul 2023 S2, 20 Jul 2023 S4, 21 Jul 2023 S2, 11 Sep 2024 S2, 12 Sep 2025 S2, 14 Sep 2025 S3, 15 Sep 2025 S1, 17 Sep 2025 S1, 17 Sep 2025 S3, 19 Sep 2025 S1, 24 Sep 2025 S3. All 11 questions below, oldest first.
Try each one first, then open its answer.
Question 1
18 Jul 2023 S2
51If the areas of two similar triangles are in the ratio 196 : 625,what would be the ratio of the corresponding sides?Tap an option to check your answer.
Question 2
20 Jul 2023 S4
56, ar and ar . If BC = 20 cm, then QR is equal to:Tap an option to check your answer.
Question 3
21 Jul 2023 S2
71The sides of two similar triangles are in the ratio 5:7. The areas of these triangles are in the ratio:Tap an option to check your answer.
Question 4
11 Sep 2024 S2
54If the ratio of the areas of two similar triangles is 25 : 144, the ratio of their corresponding sides is:Tap an option to check your answer.
Question 5
12 Sep 2025 S2
72Two triangles are similar with sides in the ratio 3:5. What is the ratio of their areas?Tap an option to check your answer.
Question 6
14 Sep 2025 S3
71In similar triangles, the ratio of corresponding altitudes is 2:5. What is the ratio of their areas?Tap an option to check your answer.
Question 7
15 Sep 2025 S1
71A right triangle has sides 3, 4, and 5. A smaller triangle is drawn inside it with its vertices on the sides of the larger triangle, such that it is similar to the larger triangle. If its perimeter is 6, what is its area?Tap an option to check your answer.
Question 8
17 Sep 2025 S1
70The area of a triangle ABC is . If a similar triangle DEF has sides that are twice the length of ABC's sides, what is the area of DEF?Tap an option to check your answer.
Question 9
17 Sep 2025 S3
70The ratios of the perimeters of two similar triangles are expressed as of . Together, their areas total 34 . What is the area of the larger triangle?Tap an option to check your answer.
Question 10
19 Sep 2025 S1
69A right-angled triangle has a hypotenuse of 13 cm and one leg of 5 cm. A second right-angled triangle is similar to the first, and its hypotenuse is 39 cm. What is the area of the second triangle?Tap an option to check your answer.
Question 11
24 Sep 2025 S3
61Two similar hexagons have their perimeters in the ratio . If the smaller hexagon has an area of , what is the area of the larger hexagon?Tap an option to check your answer.