A student is walking to school and sees a mirror on the ground. She stops a short distance from the mirror to practice her geometry. She knows her own height and the height of the school. She also knows the distance from the mirror to the school from a previous geometry activity. She would like to calculate the distance she is standing from the mirror.

- The height of the school is 20 ft.
- The distance from the school to the mirror is 50 ft.
- The height of the student is 5 ft.

What is the distance \( d \) between the student and the mirror?

Your classmate solved the problem as shown below. Did they do the work correctly?

- Equation: \(\frac{20}{50} = \frac{5}{d}\)
- Solution: \(50d = 100\)
- Conclusion: \(d = 2\) ft

Is the solution correct?

The problem can be solved using similar triangles. The student, the mirror, and the school form two similar triangles. The ratio of the sides in one triangle is equal to the ratio of the sides in the other triangle.

Let’s denote:

h1 = height of the student = 5 ft

h2 = height of the school = 20 ft

d1 = distance from the student to the mirror (which we want to find)

d2 = distance from the mirror to the school = 50 ft

The ratios of the sides of the triangles give us the equation:

h1/d1 = h2/d2

We can solve this equation for d1:

d1 = h1 * d2 / h2

Substituting the given values:

d1 = 5 ft * 50 ft / 20 ft = 12.5 ft

So, the student is standing 12.5 ft away from the mirror.