A person 1.50 m tall stands 1.20 m from the edge of a well that is 1.00 m wide. How deep is the well?

Question

ScanSolve AI Tutor · Accepted Answer

To find the depth of the well, we can use the principle of similar triangles.

Identify the two similar right-angled triangles in the diagram.
The first triangle is formed by the person's height, the horizontal distance from the person to the edge of the well, and the line of sight.
The second triangle is formed by the depth of the well, the width of the well, and the line of sight.
Extract the known dimensions from the image.
- Height of the person (vertical side of the first triangle) $= 1.50 \text{ m}$
- Horizontal distance from the person to the well's edge (horizontal side of the first triangle) $= 1.20 \text{ m}$
- Width of the well (horizontal side of the second triangle) $= 1.00 \text{ m}$
- Depth of the well (vertical side of the second triangle) $= X$ (unknown)
Set up the proportion using similar triangles.
Since the triangles are similar, the ratio of their corresponding sides is equal:
$\frac{\text{Height of person}}{\text{Distance from person to well edge}} = \frac{\text{Depth of well}}{\text{Width of well}}$ $\frac{1.50 \text{ m}}{1.20 \text{ m}} = \frac{X}{1.00 \text{ m}}$
Solve for $X$ .
$X = \frac{1.50}{1.20} \times 1.00 \text{ m}$ $X = \frac{1.5}{1.2} \text{ m}$ $X = 1.25 \text{ m}$
The depth of the well is $\text{1.25 m}$ .

Answer