A homeowner wishes to replace the three identical steps leading to her front door with a ramp - Junior Cycle Mathematics - Question Question 1 - 2012

Each step is 35 cm long, and there are three steps. Therefore, the total horizontal distance (D) is:

$$D = 3 imes 35 ext{ cm} = 105 ext{ cm}$$

The length of the ramp (L) can be found using the Pythagorean theorem:

$$L = \\sqrt{D^2 + H^2}$$

Substituting the values for D and H:

$$L = \\sqrt{(105 ext{ cm})^2 + (30 ext{ cm})^2}$$

Calculating the squares gives:

$$L = \\sqrt{11025 + 900} = \\sqrt{11925} \\approx 109.2 ext{ cm}$$

Thus, the length of the ramp is approximately 109.2 cm.