Question

find the value of a in the parallelogram.
(the parallelogram has sides labeled: ab: 2a - 19.9, bc: a - 3.5, cd: a + 1.1, ad: 17.5)
a = 21
(type an integer or a decimal.)
ab = 22.1
(type an integer or a decimal.)
bc = 17.5
(type an integer or a decimal.)
cd = \boxed{}
(type an integer or a decimal.)

Explanation:

Step1: Recall properties of parallelogram

In a parallelogram, opposite sides are equal. So, \( AB = CD \) and \( BC = AD \). We know \( AB = 2a - 19.9 \) and \( CD = a + 1.1 \), also \( BC = a - 3.5 \) and \( AD = 17.5 \). First, we can use \( BC = AD \) to find \( a \) (but we already know \( a = 21 \) from previous, now find \( CD \) which is equal to \( AB \) or use \( CD = a + 1.1 \)).

Step2: Calculate \( CD \)

Since \( AB = CD \) (opposite sides of parallelogram) and \( AB = 22.1 \), or we can use \( CD = a + 1.1 \). Substitute \( a = 21 \) into \( a + 1.1 \), we get \( 21 + 1.1 = 22.1 \). Also, since \( AB = 22.1 \) and \( AB = CD \), \( CD = 22.1 \).

Answer:

22.1