Question

7. (a) A homeowner wishes to replace the three identical steps leading to her front door with a ramp. Each step is 10 cm high and 35 cm long. Find the length of the ramp. Give your answer correct to one decimal place.​

Answer 1

The length of the ramp that will replace the three identical steps, each 10 cm high and 35 cm long, is approximately 109.2 cm when calculated using the Pythagorean theorem.

Step-by-step explanation:

The homeowner wishes to replace three identical steps with a ramp. To calculate the length of the ramp, which will form the hypotenuse of a right triangle, we use the Pythagorean theorem. Given that each step is 10 cm high and 35 cm long, we first calculate the total height (rise) and length (run) of the steps to use in our formula.

• Total height (rise) = 10 cm × 3 steps = 30 cm
• Total length (run) = 35 cm × 3 steps = 105 cm

Using the Pythagorean theorem:
hypotenuse2 = rise2 + run2
, which in our case is:
ramp length2 = 302 + 1052
. It simplifies to ramp length2 = 900 + 11025 = 11925
. Then, we take the square root of 11925 to find the length of the ramp:

Ramp length = √11925 ≈ 109.2 cm

Therefore, the ramp should be approximately 109.2 cm in length, correct to one decimal place.

Answer 2

Answer: To replace the three steps with a ramp, the height of the ramp must be equal to the total height of the steps. Since each step is 10 cm high, the total height of the three steps is 3 * 10 = 30 cm.

The length of the ramp must be equal to the length of the steps, since the ramp is replacing them. Since each step is 35 cm long, the total length of the three steps is 3 * 35 = 105 cm.

So the length of the ramp to replace the three steps leading to the front door is 105 cm, correct to one decimal place.

Step-by-step explanation: