Answer:
The error in the calculation of the area will be 2 square feet.
Step-by-step explanation:
Let the actual length of the square is L ft.
So, actual area A = L² ......... (1)
Now, if there is an error in measuring length is ΔL, then
(A + ΔA) = (L + ΔL)² {Since if there is an error in length by ΔL, then there will be an error in the calculation of area by ΔA}
⇒ A + ΔA = L² + 2×L×ΔL + (ΔL)²
Now, by linear approximation, neglect the term (ΔL)² as it will be very small.
So, A + ΔA = A + 2×L×ΔL {Since A = L²}
⇒ ΔA = 2×L×ΔL .......... (2)
Now, given that L = 10 ft and ΔL = 0.1 ft.
Hence, ΔA = 2× 10× 0.1 = 2 sq. ft.
Therefore, the error in the calculation of the area will be 2 square feet. (Answer)
