Find the whole-number possibilities for the lengths of the bases of a trapezoid with a height of 1 m and an area of 3 m2.
3 m squaredExplain how you found your answer.
The formula for the area of a trapezoid is A = (1/2)(b1 + b2)h, where b1 and b2 are the lengths of the bases and h is the height.
We can rearrange this formula to solve for b1 and b2:
b1 = 2A/h - b2
b2 = 2A/h - b1
Substituting in the given values, we get:
b1 = 2(3)/1 - b2
b2 = 2(3)/1 - b1
We can solve this system of equations by setting b1 = x and b2 = y, and then solving for x and y.
x + y = 6
x = 6 - y
Substituting x into the second equation, we get:
y = 6 - y
2y = 6
y = 3
Substituting y into the first equation, we get:
x = 6 - 3
x = 3
Therefore, the lengths of the bases of the trapezoid are 3 m and 3 m.