A phone screen is similar to a tablet screen.
<br>
The area of the tablet screen is 420 cm².
<br>
A screen costs £7000 per square metre.
<br>
Work out the cost of a screen for the phone.

**1. Find the Linear Scale Factor (LSF)** The shapes are similar, so the ratio of their corresponding sides is constant. We can use the heights. LSF (from tablet to phone) = height of phone / height of tablet = 6 / 15 = 0.4. **2. Find the Area Scale Factor (ASF)** The ratio of the areas of similar shapes is the square of the linear scale factor. ASF = (LSF)² = (0.4)² = 0.16. **3. Find the Area of the Phone Screen** Area of phone = Area of tablet × ASF Area of phone = 420 cm² × 0.16 = 67.2 cm². **4. Calculate the Cost** The cost is £7000 per square metre. We need to find the cost for an area of 67.2 cm². We must work in consistent units. Let's convert the cost to be per cm². 1 m = 100 cm 1 m² = (100 cm) × (100 cm) = 10,000 cm². Cost per cm² = £7000 / 10,000 = £0.70 per cm². Cost of phone screen = Area of phone × Cost per cm² Cost = 67.2 × 0.70 = £47.04. The cost of the screen for the phone is £47.04.