A builder is to build a staircase up to a landing which is 3 metres from the floor level. Each step rises 20 cm, and the horizontal part of the step goes 25 cm.
a) How many steps will he need to build?
b) How far from the wall will he need to move to be able to have the correct number of steps?
c) How many linear metres of carpet will he need to be able to cover all the steps and one metre at the top landing?
3m = 300cm
a) 300cm * 1step/20cm = 15 steps
b) 15 steps * 25cm/step = 375cm
c) 15(20cm + 25cm) = 6.75 m
oops - add the extra 75cm for the top landing (25cm included by thinking of it as a step)
add the extra 75cm for the top landing (25cm included by thinking of it as a step)
what does that mean?
each step as a 20cm rise and a 25cm tread
The top step is not just a step - it is the landing, but I already added in the 25cm by considering it a step.
c'mon, guy.
To answer these questions, we need to calculate the height of the staircase, the number of steps, the horizontal distance required, and the linear meters of carpet needed.
a) To determine the number of steps needed, we first need to calculate the total height of the staircase. Given that each step rises 20 cm, we can divide the height of the landing (3 meters) by the height of each step (0.2 meters):
Number of steps = Height of landing / Height of each step
= 3 m / 0.2 m
= 15 steps
Therefore, the builder will need to build 15 steps.
b) To determine the horizontal distance required, we need to calculate the length of each step and multiply by the number of steps. Given that the horizontal part of the step goes 25 cm, we can multiply this by the number of steps:
Horizontal distance = Length of each step * Number of steps
= 0.25 m * 15
= 3.75 meters
Therefore, the builder will need to move 3.75 meters from the wall to have the correct number of steps.
c) To calculate the linear meters of carpet required, we need to consider the horizontal length of each step and the one meter at the top landing. Given that the horizontal part of the step goes 25 cm and there are 15 steps, we can calculate the total linear meters of carpet needed:
Linear meters of carpet = (Length of each step * Number of steps) + Length of top landing
= (0.25 m * 15) + 1 m
= 3.75 meters + 1 meter
= 4.75 meters
Therefore, the builder will need 4.75 linear meters of carpet to cover all the steps and one meter at the top landing.