Calculate Wallpaper Price: Scaling from 240x360 to 1200x1800 Dimensions

Q: Why do I need to square the scaling factor?

Because wallpaper covers area, not just length! When both length and width scale by factor 5, the total area scales by $ 5 \times 5 = 5^2 = 25 $. Think of it like a square: doubling each side makes it 4 times bigger, not 2 times.

Q: How do I find the scaling factor?

Divide the new dimension by the old dimension: $ \frac{1200}{240} = 5 $ or $ \frac{1800}{360} = 5 $. Both dimensions should give you the same scaling factor if they're proportional!

Q: What if the dimensions aren't proportional?

Check your problem again! For similar rectangles, both length and width must scale by the same factor. If they don't, you might have copied the numbers incorrectly.

Q: Can I solve this by calculating areas directly?

Absolutely! Calculate $ 240 \times 360 = 86400 $ and $ 1200 \times 1800 = 2160000 $. Then find the ratio: $ \frac{2160000}{86400} = 25 $, so price = $ 1140 \times 25 = 28500 $.

Q: Why does wallpaper pricing work this way?

Wallpaper is sold by area coverage - you pay for how much wall surface it covers. More area means more material, so the price increases proportionally with the total area, not just the dimensions.

Area Scaling with Proportional Ratios

The price of 240X360 wallpaper is 1140. What is the price of 1200X1800 wallpaper?

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Step-by-step video solution

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00:00 Calculate the price of the large wallpaper

00:03 Find the similarity ratio

00:12 According to the sides ratio, we showed that the polygons are similar

00:23 The area ratio equals the similarity ratio squared

00:30 Make sure to square both numerator and denominator

00:39 The payment ratio equals the area similarity ratio

00:53 And this is the solution to the question

Step-by-step written solution

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Understand the problem

The price of 240X360 wallpaper is 1140. What is the price of 1200X1800 wallpaper?

Final Answer

28500

Key Points to Remember

Essential concepts to master this topic

Scaling Rule: When dimensions scale by factor k, area scales by $k^2$
Technique: Find ratio: 1200÷240 = 5, then calculate 1140 × $5^2$ = 28500
Check: Verify area ratio matches price ratio: 25 times larger area = 25 times higher price ✓

Common Mistakes

Avoid these frequent errors

Using linear scaling instead of area scaling
Don't just multiply by the dimension ratio like 1140 × 5 = 5700! This ignores that wallpaper pricing depends on total area, not just one dimension. Always square the scaling factor because area = length × width.

Practice Quiz

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FAQ

Everything you need to know about this question

Why do I need to square the scaling factor?

Because wallpaper covers area, not just length! When both length and width scale by factor 5, the total area scales by $5 \times 5 = 5^2 = 25$ . Think of it like a square: doubling each side makes it 4 times bigger, not 2 times.

How do I find the scaling factor?

Divide the new dimension by the old dimension: $\frac{1200}{240} = 5$ or $\frac{1800}{360} = 5$ . Both dimensions should give you the same scaling factor if they're proportional!

What if the dimensions aren't proportional?

Check your problem again! For similar rectangles, both length and width must scale by the same factor. If they don't, you might have copied the numbers incorrectly.

Can I solve this by calculating areas directly?

Absolutely! Calculate $240 \times 360 = 86400$ and $1200 \times 1800 = 2160000$ . Then find the ratio: $\frac{2160000}{86400} = 25$ , so price = $1140 \times 25 = 28500$ .

Why does wallpaper pricing work this way?

Wallpaper is sold by area coverage - you pay for how much wall surface it covers. More area means more material, so the price increases proportionally with the total area, not just the dimensions.

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