Question

1. determine the length of the other base of each of these trapezoids. a. median of 14\frac{3}{16} in. and one base of 21\frac{1}{16} in. b. median of 8.36 m and one base of 0.78 m

Explanation:

Step1: Recall the formula for the median of a trapezoid

The formula for the median \(M\) of a trapezoid is \(M=\frac{b_1 + b_2}{2}\), where \(b_1\) and \(b_2\) are the lengths of the bases. We can solve for \(b_2\) as \(b_2 = 2M−b_1\).

Step2: Solve for part (a)

First, convert the mixed numbers to improper fractions. \(M = 14\frac{3}{16}=\frac{14\times16 + 3}{16}=\frac{224+3}{16}=\frac{227}{16}\) and \(b_1=21\frac{1}{16}=\frac{21\times16 + 1}{16}=\frac{336 + 1}{16}=\frac{337}{16}\).
Using \(b_2 = 2M−b_1\), we have \(2M=2\times\frac{227}{16}=\frac{227}{8}=\frac{454}{16}\).
Then \(b_2=\frac{454}{16}-\frac{337}{16}=\frac{454 - 337}{16}=\frac{117}{16}=7\frac{5}{16}\) inches.

Step3: Solve for part (b)

Using the formula \(b_2 = 2M−b_1\), with \(M = 8.36\) and \(b_1=0.78\).
\(2M=2\times8.36 = 16.72\).
Then \(b_2=16.72- 0.78=15.94\) meters.

Answer:

a. \(7\frac{5}{16}\) inches
b. \(15.94\) meters