Question

figure abcd is a kite. what is the length of line segment cd? 7 units 8 units 28 units 35 units

Explanation:

Step1: Use the property of a kite

In a kite, two pairs of adjacent sides are equal. Here, \(AB = BC = 22\) (given), and \(AD = CD\). Also, \(AB = 3x + 1\) and \(AD=4x\). Since \(AB = BC\) is not used for finding \(x\) directly (as we use the relation between \(AB\) and \(AD\) for the non - equal adjacent sides in terms of \(x\)). Wait, no, actually in a kite, two pairs of adjacent sides are equal. So \(AB = BC\) (given as \(AB = 3x + 1\) and \(BC = 22\)), so \(3x+1 = 22\).
$$3x+1 = 22$$

Step2: Solve for \(x\)

Subtract \(1\) from both sides:
$$3x=22 - 1=21$$
Divide both sides by \(3\):
$$x=\frac{21}{3}=7$$

Step3: Find the length of \(CD\)

Since \(CD = AD\) and \(AD = 4x\), substitute \(x = 7\) into \(4x\).
$$CD=4x=4\times7 = 28$$

Answer:

28 units