NavGanitMateby NavGreen Compute, AustraliaBased on Victorian Curriculum Mathematics v2.0
← Back to practice

Shape algorithms

Wide tables scroll horizontally. For detailed working, you may prefer a larger screen.

Required skills (click to reveal)

In a community garden in Melbourne, a triangular flower bed is designed using three wooden frames. The frames have lengths of 68 cm, 59 cm, and 75 cm.

A student is creating an algorithm to determine if this triangle is similar to another triangle with side lengths 136 cm, 118 cm, and 150 cm. The algorithm checks for similarity using the SSS (side-side-side) similarity criterion, which requires that the ratios of corresponding sides are equal.

What is the exact ratio of the corresponding sides of the two triangles, expressed as a simplified fraction?

Concept illustrations

These are separate worked examples of related concepts, not a diagram of this question. Their values and dimensions do not describe your question.

Classifying from known properties. For a quadrilateral already known to have four right angles, check whether all four sides are equal. Yes gives a square; no gives a rectangle that is not a square. A square remains a rectangle too.4 right anglesRectangle→4 equal sides?Check lengths→Yes: squareNo: non-square
For a quadrilateral already known to have four right angles, check whether all four sides are equal. Yes gives a square; no gives a rectangle that is not a square. A square remains a rectangle too.

Press Start when ready. Time includes time spent in another tab. Submit your answer before opening a help panel for a timed rank.

00:00
0 wordsOnly your numerical final answer or selected MCQ option is checked. Scratch working is not graded.

Report a problem or suggest an improvement

My notes — optional, not graded 0 words

Notes and scratch working stay in this browser and are linked to this question version. They are not graded or included in feedback. On shared devices, other people using this browser may see them.

For this question only. Your full notebook is on the dashboard.

Notes save in this browser. Download a copy to keep them elsewhere.

Report a problem or suggest an improvement

Your observations help improve this question. You can report an issue or recommend a better explanation, visual or experience.

0 words

The report includes your message and question/version details. Saved profile details, answers, notes and attempt history are not automatically attached. Leave out names and contact details, and check screenshots for personal information and embedded metadata.

Attachments may contain personal information. Review them before sharing. Logs collect only event codes and timestamps after you enable them. Download the ZIP to keep a copy, then attach it to an email if you choose.

Formula and explanation (click to reveal)

Opening this before your first submission makes the attempt practice only.

Formula

Explanation

Worked solution and answer (click to reveal)

Opening this before your first submission makes the attempt practice only.

Worked solution

  1. The first triangle has side lengths 68 cm, 59 cm, and 75 cm. The second triangle has side lengths 136 cm, 118 cm, and 150 cm. We are to determine if they are similar using the SSS similarity criterion, which requires that the ratios of corresponding sides are equal.
  2. To apply SSS similarity, we must pair corresponding sides. We assume the sides are ordered in increasing length for comparison: 59 cm, 68 cm, 75 cm for the first triangle; 118 cm, 136 cm, 150 cm for the second.
  3. Calculate the ratio of the smallest sides: 118 / 59 = 2.0. This suggests a possible scale factor of 2.
  4. Check the ratio of the middle sides: 136 / 68 = 2.0. This matches the previous ratio.
  5. Check the ratio of the largest sides: 150 / 75 = 2.0. This also matches.
  6. Since all three ratios are exactly 2.0, the triangles are similar by the SSS similarity criterion.
  7. The ratio of corresponding sides is 2.0, which as a fraction is 2/1.
  8. Simplify 2/1: it is already in simplest form.
  9. Verify by cross-multiplication: 118 / 59 = 2, 136 / 68 = 2, 150 / 75 = 2. All confirm the same ratio.
  10. The ratio of corresponding sides is exactly 2:1, or 2/1.
  11. The algorithm correctly identifies similarity because all three side ratios are equal. The exact ratio is 2/1.
  12. The final answer is 2/1, as the simplified fraction of the side ratios.

Reference answer: 2/1

Alternative methods (click to reveal)

Shortcuts are shown only when applicable. Check the conditions before using one.

Earlier attempts for this question

#Date / timeYour answerResultSecondsHelp revealedRank
History stays in this browser when storage is available. Export it to your shared Drive folder and import it on another computer.
Worksheet details

Naming pattern: Topic_Grade_Complexity_YYYYMMDD_HH24MISS.html

Validation compares your answer with the generated reference. The model's reference can be wrong. Time ranks use an estimated student solving time, not a measured benchmark or a comparison with other students. An incorrect answer receives no speed rank.

NavGanitMate privacy & saved work

Saved in this browser. Your profile preferences, answers, practice history and notes are stored here when browser storage is available. They are not automatically uploaded to our servers. People sharing this browser may see saved work; changing the learner name does not create a separate private account. A nickname is enough.

Keep copies of important work. Clearing browser data, private browsing or changing browser or device can mean losing saved work. Download notes and export history separately. Downloads are copies of the selected content, not a complete account backup; not every format can be imported to restore your work. Keep these files somewhere private.

Visiting the website. Cloudflare helps deliver and protect this site and processes connection information such as IP addresses and requested pages. Server error logs may also contain request details. Security features may use cookies. This is separate from your browser-saved learning records. Cloudflare privacy information.

A parent-connection reminder uses a local list of up to five completed question IDs for this browser profile and a tab-session dismissal marker. Reminder activity is not uploaded and practice remains available.

Sharing feedback is your choice. A report includes your message and question/version details. Your saved profile, answers and notes are not automatically attached. Files you select can reveal personal details or contain embedded metadata: check and redact them before sharing. Diagnostic event codes and timestamps are included only after you enable logging. Sending email shares your message and attachments with the recipient and email providers. A download alone sends nothing to us. Website feedback delivery may be unavailable; only a confirmed receipt indicates it was received.