Question

1-1 A carpet is to be installed in a room whose length is measured to be 12.71 m and whose width is measured to be 5.46 m. Find the area and error in the area of the room. (∆L=0.01)

Answer 1

Step-by-step explanation:

Area of the room = Length × Width

Given

Length = 12.71m

Width = 5.46m

Area of the room = 12.71m×5.46m

Area of the room = 69.3966m²

To get the area of the error, we will use the relationship;

∆A/A = {∆L/L + ∆W/W}

∆A/A = {0.01/12.71 + 0.01/5.46}

∆A/A = {0.0007868+ 0.001832}

∆A/A = 0.0026182

∆A = 0.0026182A

Since Area A = 69.3966m²

∆A = 0.0026182(69.3966)

∆A ≈ 0.1817m²

Hence error in the area of the room is 0.1817m²