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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.

  1. Question 1

    18 Jul 2023 S2

    51
    If the areas of two similar triangles are in the ratio 196 : 625,what would be the ratio of the corresponding sides?

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  2. Question 2

    20 Jul 2023 S4

    56
    ΔABC∼ΔPQR\Delta ABC \sim \Delta PQR, ar (ΔABC)=16 cm2(\Delta ABC) = 16\ \text{cm}^2 and ar (ΔPQR)=25 cm2(\Delta PQR) = 25\ \text{cm}^2. If BC = 20 cm, then QR is equal to:

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  3. Question 3

    21 Jul 2023 S2

    71
    The sides of two similar triangles are in the ratio 5:7. The areas of these triangles are in the ratio:

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  4. Question 4

    11 Sep 2024 S2

    54
    If the ratio of the areas of two similar triangles is 25 : 144, the ratio of their corresponding sides is:

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  5. Question 5

    12 Sep 2025 S2

    72
    Two triangles are similar with sides in the ratio 3:5. What is the ratio of their areas?

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  6. Question 6

    14 Sep 2025 S3

    71
    In similar triangles, the ratio of corresponding altitudes is 2:5. What is the ratio of their areas?

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  7. Question 7

    15 Sep 2025 S1

    71
    A 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?

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  8. Question 8

    17 Sep 2025 S1

    70
    The area of a triangle ABC is 16 cm216\ \text{cm}^2. If a similar triangle DEF has sides that are twice the length of △\triangleABC's sides, what is the area of △\triangleDEF?

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  9. Question 9

    17 Sep 2025 S3

    70
    The ratios of the perimeters of two similar triangles are expressed as of 3:53 : 5. Together, their areas total 34 cm2\text{cm}^2. What is the area of the larger triangle?

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  10. Question 10

    19 Sep 2025 S1

    69
    A 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?

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  11. Question 11

    24 Sep 2025 S3

    61
    Two similar hexagons have their perimeters in the ratio 5:75:7. If the smaller hexagon has an area of 75 cm275 \text{ cm}^2, what is the area of the larger hexagon?

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