- The problem involves similar triangles formed by the sun's rays casting shadows.
- The house and its shadow form one right triangle, with a height of 16 ft and a base (shadow) of 24 ft.
- The fence and its shadow form a smaller, similar right triangle, with a height of 4 ft and an unknown shadow length.
- Since the triangles are similar, their corresponding sides are proportional.
- Set up the proportion: (height of house) / (shadow of house) = (height of fence) / (shadow of fence).
- Substitute the known values: 16 / 24 = 4 / x, where x is the unknown shadow length of the fence.
- Simplify the left side: 16/24 reduces to 2/3.
- So, 2/3 = 4/x.
- Cross-multiply: 2 * x = 3 * 4.
- This gives: 2x = 12.
- Solve for x: x = 12 / 2.
- Therefore, x = 6.
- The shadow of the fence is 6 feet long.
Parent Tip: Review the logic above to help your child master the concept of similar triangles word problems worksheet.
