find the whole-number possibilities for the lengths of the bases of a trapezoid with a height of 1m and an area of 3m squared. Explain how you found your answer
To find the whole-number possibilities for the lengths of the bases of a trapezoid with a height of 1m and an area of 3m², we can use the formula for the area of a trapezoid:
Area = (1/2) * (base1 + base2) * height
Given that the height is 1m and the area is 3m², we can substitute these values into the formula and rearrange it to solve for the possible values of the bases.
3 = (1/2) * (base1 + base2) * 1
Simplifying the equation further:
2 * 3 = base1 + base2
6 = base1 + base2
Now let's list the possible whole-number combinations for base1 and base2 whose sum is equal to 6:
1. base1 = 1m, base2 = 5m
2. base1 = 2m, base2 = 4m
3. base1 = 3m, base2 = 3m
4. base1 = 4m, base2 = 2m
5. base1 = 5m, base2 = 1m
So, the whole-number possibilities for the lengths of the bases of the trapezoid with a height of 1m and an area of 3m² are (1m, 5m), (2m, 4m), (3m, 3m), (4m, 2m), and (5m, 1m).
To find these possibilities, we used the formula for the area of a trapezoid and rearranged it to solve for the bases. Then, we listed all the possible combinations of whole numbers whose sum is equal to the value we obtained for the sum of the bases.