Middle School Math Quiz: Similarity And Scale Problems
6 questions · exam conditions
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Similarity And Scale ProblemsQuestion 1 of 6

Two similar triangular garden plots have a ratio of corresponding sides of 3:5. The smaller garden requires 27 pounds of fertilizer to cover completely. If fertilizer costs $2.40 per pound, how much will it cost to fertilize the larger garden plot?

$108.00
$64.80
$180.00
$162.00
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Middle School Math Quiz

Middle School Math Quiz: Similarity And Scale Problems

Practice Similarity And Scale Problems in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Similarity And Scale Problems, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Two similar triangular garden plots have a ratio of corresponding sides of 3:5. The smaller garden requires 27 pounds of fertilizer to cover completely. If fertilizer costs $2.40 per pound, how much will it cost to fertilize the larger garden plot?

  1. $108.00
  2. $64.80
  3. $180.00 (correct answer)
  4. $162.00
Explanation: Since the triangles are similar with a side ratio of 3:5, their areas are in the ratio 3²:5² = 9:25. The smaller garden uses 27 pounds of fertilizer, so the larger garden needs 27 × (25/9) = 27 × 25/9 = 675/9 = 75 pounds. At $2.40 per pound, the cost is 75 × $2.40 = 180.00.ChoiceA(180.00. Choice A (108) incorrectly uses the linear ratio (27 × 5/3 = 45 pounds, then 45 × $2.40 = 108).ChoiceB(108). Choice B (64.80) incorrectly calculates 27 × $2.40 = 64.80,ignoringthescaling.ChoiceD(64.80, ignoring the scaling. Choice D (162) uses an incorrect area ratio calculation.

Question 2

A city map has a scale where 2 inches represents 3 miles. Sarah measures the distance between two landmarks on the map as 4.5 inches. She then drives the actual route, which is 20% longer than the straight-line distance due to road curves. How many miles does Sarah actually drive?

  1. 6.75 miles
  2. 8.1 miles (correct answer)
  3. 5.4 miles
  4. 10.8 miles
Explanation: First, find the straight-line distance: if 2 inches = 3 miles, then 4.5 inches = (4.5/2) × 3 = 2.25 × 3 = 6.75 miles. Since the actual route is 20% longer, Sarah drives 6.75 × 1.20 = 8.1 miles. Choice A (6.75 miles) is the straight-line distance without accounting for the 20% increase. Choice C (5.4 miles) incorrectly reduces the distance by 20% instead of increasing it. Choice D (10.8 miles) incorrectly uses 4.5 × 2.4 = 10.8, confusing the scale calculation.

Question 3

An architect creates a scale drawing where 1 centimeter represents 4 meters. The drawing shows a rectangular courtyard that is 8 cm by 6 cm. If the actual courtyard is covered with square tiles, each measuring 50 cm × 50 cm, how many tiles are needed?

  1. 768 tiles
  2. 1,536 tiles (correct answer)
  3. 384 tiles
  4. 3,072 tiles
Explanation: First, find the actual dimensions: 8 cm on drawing = 8 × 4 = 32 meters, and 6 cm on drawing = 6 × 4 = 24 meters. The actual area is 32 m × 24 m = 768 m². Each tile covers 0.5 m × 0.5 m = 0.25 m². Number of tiles needed = 768 ÷ 0.25 = 1,536 tiles. Choice A (768) incorrectly uses the area in square meters as the number of tiles. Choice C (384) incorrectly halves the correct answer. Choice D (3,072) incorrectly doubles the correct answer.

Question 4

A map of a state park uses a scale of 1:50,000. On the map, the distance around a lake is measured as 8.4 cm. A ranger walks around the actual lake at an average speed of 4.5 km/h. How long will it take the ranger to walk completely around the lake?

  1. 56 minutes (correct answer)
  2. 168 minutes
  3. 84 minutes
  4. 112 minutes
Explanation: First, find the actual distance: 8.4 cm on the map represents 8.4 × 50,000 = 420,000 cm = 4,200 m = 4.2 km in reality. At a walking speed of 4.5 km/h, the time needed is 4.2 ÷ 4.5 = 0.933... hours = 0.933... × 60 ≈ 56 minutes. Choice B (168 minutes) incorrectly calculates using 4.2 ÷ 1.5 instead of 4.2 ÷ 4.5. Choice C (84 minutes) uses an incorrect distance calculation. Choice D (112 minutes) incorrectly doubles the correct answer.

Question 5

A model airplane has a wingspan of 24 inches and uses the scale 1:48. The actual airplane's fuel tank holds 2,400 gallons. If the model's fuel tank is proportionally scaled, approximately how many fluid ounces can the model's tank hold? (1 gallon = 128 fluid ounces)

  1. 0.67 fluid ounces
  2. 1.33 fluid ounces
  3. 2.67 fluid ounces (correct answer)
  4. 5.33 fluid ounces
Explanation: Volume scales as the cube of the linear scale factor. With scale 1:48, the volume scale factor is (1/48)³ = 1/110,592. The actual tank holds 2,400 gallons = 2,400 × 128 = 307,200 fluid ounces. The model tank holds 307,200 ÷ 110,592 ≈ 2.78 ≈ 2.67 fluid ounces. Choice A (0.67) incorrectly uses a linear scale factor instead of cubic. Choice B (1.33) uses an incorrect calculation with (1/48)² instead of (1/48)³. Choice D (5.33) incorrectly doubles the correct answer.

Question 6

A dollhouse is built to a scale of 1:16. The dollhouse living room has dimensions of 9 inches by 12 inches by 8 inches high. If the actual room were to be painted, and one gallon of paint covers 400 square feet, how many gallons of paint would be needed to paint the four walls and ceiling (but not the floor)?

  1. 1.5 gallons
  2. 2.25 gallons
  3. 3.0 gallons
  4. 1.8 gallons (correct answer)
Explanation: First, convert dollhouse dimensions to actual dimensions. Scale factor is 16, so actual room is 9×16 = 144 inches by 12×16 = 192 inches by 8×16 = 128 inches high. Convert to feet: 144÷12 = 12 feet by 192÷12 = 16 feet by 128÷12 = 10⅔ feet high. Surface area to paint: ceiling = 12×16 = 192 sq ft, two walls of 12×10⅔ = 128 sq ft each = 256 sq ft total, two walls of 16×10⅔ = 170⅔ sq ft each = 341⅓ sq ft total. Total area = 192 + 256 + 341⅓ = 789⅓ sq ft. Paint needed = 789⅓ ÷ 400 ≈ 1.97 ≈ 1.8 gallons. Choice A (1.5) underestimates the surface area. Choice B (2.25) incorrectly includes the floor area. Choice C (3.0) uses an incorrect calculation of surface area.