Math With AmarA C A D E M Y

Grade 10 · Connect similarity powers · 345 of 750

Connect similarity powers · practice 36

Dilate a rectangle with sides 1 and 5.75 by length factor 3. Find the new side lengths and area. 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

Dilate a rectangle with sides 1 and 5.75 by length factor 3. Find the new side lengths and area.

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
Connect similarity powers · practice 36. Current length multiplier: 1. Current width: 1. Current area: 5.75. Final area multiplier: 9One length multiplier, two changing dimensionsOriginal dimensions: 1 by 5.75Current k = 1; area = 5.75Dashed: original · solid: dilated image
Only positive uniform dilations are shown. The axis drawing scale is equal horizontally and vertically and remains fixed during playback. The dashed original and solid image share the lower-left corner as dilation center.

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.

Current length multiplier
1
Current width
1
Current area
5.75
Final area multiplier
9

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

A dilation multiplies every length by the same positive factor. Ratios of corresponding sides stay equal, but area changes by the square of that factor because two independent dimensions both change. A scale below one shrinks the figure without changing its shape. Starting quantities: Original width = 1; Original height = 5.75; Length scale factor k = 3.

new lengths = k × old lengths; new area = k² × old area

03 · Reflect and transfer

Explain what changes and why.

Why is a length scale factor different from an area scale factor?

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.