To solve this problem, we need to find the sum of the lengths of the bases of a trapezium given its altitude and area. Here are the steps:
1. Convert Altitude from cm to meters:
The given altitude of the trapezium is 17 cm. We need to convert this to meters (since the area is given in square meters).
[tex]\[
\text{altitude in meters} = \frac{17 \text{ cm}}{100} = 0.17 \text{ m}
\][/tex]
2. Recall the Formula for the Area of a Trapezium:
The formula for the area [tex]\(A\)[/tex] of a trapezium is given by:
[tex]\[
A = \frac{1}{2} \times (\text{base}_1 + \text{base}_2) \times \text{altitude}
\][/tex]
Here, [tex]\( \text{base}_1 \)[/tex] and [tex]\( \text{base}_2 \)[/tex] are the lengths of the parallel sides, and the altitude is the distance between them.
3. Rearrange the Formula to Solve for the Sum of Bases:
To find the sum of the bases ([tex]\(\text{base}_1 + \text{base}_2\)[/tex]), we rearrange the formula:
[tex]\[
\text{base}_1 + \text{base}_2 = \frac{2 \times A}{\text{altitude}}
\][/tex]
4. Substitute the Given Values into the Formula:
We have:
- Area [tex]\(A = 0.85 \text{ m}^2\)[/tex]
- Altitude [tex]\( \text{altitude} = 0.17 \text{ m} \)[/tex]
Substituting these values into the formula, we get:
[tex]\[
\text{base}_1 + \text{base}_2 = \frac{2 \times 0.85 \text{ m}^2}{0.17 \text{ m}}
\][/tex]
5. Calculate the Sum of the Bases:
Performing the division:
[tex]\[
\text{base}_1 + \text{base}_2 = \frac{1.7 \text{ m}^2}{0.17 \text{ m}} = 10 \text{ m}
\][/tex]
So, the sum of the lengths of the bases of the trapezium is approximately [tex]\(10 \text{ meters}\)[/tex].
