Math With AmarA C A D E M Y

Grade 10 · Verify a coordinate-distance model · 52 of 750

Verify a coordinate-distance model · practice 6

A right triangle has perpendicular legs 6 and 9. Find its hypotenuse. Follow the calculation, then test the quantities in the animated example.

Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.

01 · Make a prediction

Your practice question

A right triangle has perpendicular legs 6 and 9. Find its hypotenuse.

Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.

02 · Explore the model

See the mathematical relationship move.

Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.

Watch the relationship

Paused
Verify a coordinate-distance model · practice 6. First square area: 36. Second square area: 81. Combined area revealed: 0. Hypotenuse: 10.817Square the legs, add, then take a root69Square areas3681a² + b² = 117; c = 10.817
The theorem is applied only to a Euclidean right triangle with positive leg lengths. The triangle has equal axis scale, while the area bars use a separate common scale and are not drawn on its sides.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

First square area
36
Second square area
81
Combined area revealed
0
Hypotenuse
10.817

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

The mathematical idea

For a right triangle, the square of the longest side equals the sum of the squares of the two legs. Square areas provide the comparison; the hypotenuse itself is the positive square root of their sum. Adding side lengths is not a substitute for this theorem. Starting quantities: First leg a = 6; Second leg b = 9.

c² = a²+b²; c = √(a²+b²)

03 · Reflect and transfer

Explain what changes and why.

Why does the theorem require a right angle between the two given legs?

This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.