Ratios · Scaling & similar figures · 5.4

Find a missing side.

To find a missing side of similar figures, set up a proportion of corresponding sides and solve. If 3 matches 9 and 5 matches x, then 3/9 = 5/x → x = 15.

01 / THE IDEA

See it work.

Similar figures

Same shape, scaled.

Corresponding sides are proportional — so the ratio is the same.

39
→
515

3/9 = 5/15 → the missing side is 15.

Watch the method

Find a missing side

3/9 = 5/x → x = 15.

1 / 2
39=5x\frac{3}{9} = \frac{5}{x}
1

Set up the proportion

Corresponding sides of similar figures are proportional.

39=5x\frac{3}{9} = \frac{5}{x}
2

Cross-multiply & solve

Solve for the missing side.

x=15x = 15
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 40.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

Proportion of sides

Write known side ÷ matching side = other known ÷ unknown, then cross-multiply.

Why it works

3/9 = 5/x.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

Two similar figures: a 4-side matches a 16-side. The matching figure has a 8-side — find the other side.

1

Set up the proportion

Corresponding sides of similar figures are proportional. 4/16 = 8/x

2

Cross-multiply & solve

Solve for the missing side. x = 32

EX 2medium

Two similar figures: a 5-side matches a 15-side. The matching figure has a 20-side — find the other side.

1

Set up the proportion

Corresponding sides of similar figures are proportional. 5/15 = 20/x

2

Cross-multiply & solve

Solve for the missing side. x = 60

EX 3hard

Two similar figures: a 3-side matches a 6-side. The matching figure has a 6-side — find the other side.

1

Set up the proportion

Corresponding sides of similar figures are proportional. 3/6 = 6/x

2

Cross-multiply & solve

Solve for the missing side. x = 12

04 / COMMON TRAPS

Where students slip.

Trap

Pairing the wrong sides.

Fix

Match each side with its corresponding side.

Trap

Forgetting to cross-multiply.

Fix

Solve the proportion to find the side.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

Two similar figures: a 4-side matches a 16-side. The matching figure has a 12-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
C2

Two similar figures: a 5-side matches a 20-side. The matching figure has a 10-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
C3

Two similar figures: a 5-side matches a 15-side. The matching figure has a 10-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
C4

Two similar figures: a 3-side matches a 6-side. The matching figure has a 9-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
Apply

Apply (4)

A1

Two similar figures: a 2-side matches a 6-side. The matching figure has a 8-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
A2

Two similar figures: a 3-side matches a 9-side. The matching figure has a 6-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
A3

Two similar figures: a 2-side matches a 8-side. The matching figure has a 4-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
A4

Two similar figures: a 2-side matches a 8-side. The matching figure has a 8-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
Extension

Extension (4)

E1

Two similar figures: a 2-side matches a 4-side. The matching figure has a 8-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
E2

Two similar figures: a 4-side matches a 16-side. The matching figure has a 8-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
E3

Two similar figures: a 3-side matches a 12-side. The matching figure has a 6-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.
E4

Two similar figures: a 4-side matches a 12-side. The matching figure has a 8-side — find the other side.

Need a hint?
  • Write the proportion of matching sides.
  • Cross-multiply and solve.