A person estimated the length and width of a room by counting strides. The length of his stride is 0.8 m long. He counted ten strides along the length and six strides along the width. If the actual length was 9 m and 5 m respectively, determine the percentage error made in estimating the length and width.
Answer (1)
To determine the percentage error in the estimation of the length and width of the room, we first need to compute the estimated dimensions using the person's stride.
Step 1: Calculate the estimated dimensions using the stride length.
The length of the room estimated by the person: 10 strides × 0.8 m/stride = 8 m
The width of the room estimated by the person: 6 strides × 0.8 m/stride = 4.8 m
Step 2: Calculate the percentage error for both length and width.
The percentage error is found using the formula: Percentage Error = ( Actual Value Estimated Value − Actual Value ) × 100%
For the length: Percentage Error (Length) = ( 9 m 8 m − 9 m ) × 100% = ( 9 − 1 ) × 100% ≈ − 11.11% This indicates an 11.11% underestimation of the length.
For the width: Percentage Error (Width) = ( 5 m 4.8 m − 5 m ) × 100% = ( 5 − 0.2 ) × 100% = − 4% This indicates a 4% underestimation of the width.
Therefore, the person underestimated the room's length by approximately 11.11% and the width by 4%.
