A staircase was built such that each subsequent stair has a uniform difference in height.The height of the 6th stair from the horizontal floor was 85cm and the height of the 10th was 145.calculate height of the first and uniform difference in height of the stairs.
Let's assume that the height of the first stair is H and the uniform difference in height is D.
Given that the height of the 6th stair from the horizontal floor is 85 cm, we can express this information as:
H + 5D = 85 ----- (Equation 1)
Similarly, given that the height of the 10th stair from the horizontal floor is 145 cm, we can express this information as:
H + 9D = 145 ----- (Equation 2)
To solve these two equations, we'll subtract Equation 1 from Equation 2:
(H + 9D) - (H + 5D) = 145 - 85
4D = 60
D = 60/4
D = 15
Substituting this value of D in Equation 1, we can find the value of H:
H + 5(15) = 85
H + 75 = 85
H = 85 - 75
H = 10
Therefore, the height of the first stair is 10 cm and the uniform difference in height of the stairs is 15 cm.