Math With AmarA C A D E M Y

Grade 8 · Recover a right-triangle distance · 105 of 750

Recover a right-triangle distance · practice 9

A right triangle has perpendicular legs 5 and 11. 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 5 and 11. 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
Recover a right-triangle distance · practice 9. First square area: 25. Second square area: 121. Combined area revealed: 0. Hypotenuse: 12.083Square the legs, add, then take a root511Square areas25121a² + b² = 146; c = 12.083
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
25
Second square area
121
Combined area revealed
0
Hypotenuse
12.083

HD animation studio

From experiment to screen.

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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 = 5; Second leg b = 11.

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.