College Math Placement Practice Test

What is the length of the other base of a trapezoid with an area of 864 cm², height of 24 cm, and one base length of 30 cm?

1. 42 cm

2. 45 cm

3. 114 cm

4. 38 cm

The correct answer is: 42 cm

To find the length of the other base of the trapezoid, we can use the formula for the area of a trapezoid: \[ \text{Area} = \frac{1}{2} \times (b_1 + b_2) \times h \] where \(b_1\) and \(b_2\) are the lengths of the two bases, and \(h\) is the height. We know the area (864 cm²), the height (24 cm), and one base (30 cm). First, we can rearrange the formula to solve for the sum of the bases: \[ 864 = \frac{1}{2} \times (30 + b_2) \times 24 \] Multiplying both sides by 2 to eliminate the fraction gives: \[ 1728 = (30 + b_2) \times 24 \] Next, divide both sides by 24 to isolate the term with the bases: \[ 72 = 30 + b_2 \] To find \(b_2\), subtract 30 from both sides: \[ b_2 = 72 - 30 = 42 \text{