The sides of a right angled triangle measured to the nearest cm are 5cm, 12cm and 13cm
Determine the
a) limits within which the measured dimensions lie
Since no decimal places or precision is given, I'd say all values are ±0.5
What about the percentage error of the triangle
To determine the limits within which the measured dimensions lie, we need to consider the possible range of measurement errors.
For a right-angled triangle with sides measuring 5cm, 12cm, and 13cm, we will assume that there is a potential error of ± 0.5cm in each measurement. This means that the actual lengths of the sides could be slightly larger or smaller than the measured values.
Based on this assumption, we can find the upper and lower limits for each side as follows:
1. For the first side (5cm):
- The lower limit would be 5cm - 0.5cm = 4.5cm
- The upper limit would be 5cm + 0.5cm = 5.5cm
2. For the second side (12cm):
- The lower limit would be 12cm - 0.5cm = 11.5cm
- The upper limit would be 12cm + 0.5cm = 12.5cm
3. For the third side (13cm):
- The lower limit would be 13cm - 0.5cm = 12.5cm
- The upper limit would be 13cm + 0.5cm = 13.5cm
Therefore, the limits within which the measured dimensions lie are as follows:
a) First side: 4.5cm ≤ x ≤ 5.5cm
b) Second side: 11.5cm ≤ y ≤ 12.5cm
c) Third side: 12.5cm ≤ z ≤ 13.5cm