Question

find the value of a in the parallelogram.

(image of parallelogram abcd with ab labeled 2a - 19.9, bc labeled a - 3.5, cd labeled a + 1.1, and ad labeled 17.5)

a = 21
(type an integer or a decimal.)

ab =
(type an integer or a decimal.)

Explanation:

Step1: Recall parallelogram side property

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, we are given \( a = 21 \).

Step2: Substitute a into AB's formula

Substitute \( a = 21 \) into the expression for \( AB \), which is \( 2a - 19.9 \). So \( AB = 2\times21 - 19.9 \).

Step3: Calculate the value

First, calculate \( 2\times21 = 42 \). Then, \( 42 - 19.9 = 22.1 \).

Answer:

22.1