In kite ABCD, diagonals intersect at right angles at point E. If AE = 8 cm and BD = 12 cm, find the length of side AB.
Options
A
8.5 cm
B
9.2 cm
C
10 cm
D
11 cm
Answer & Analysis
Answer
C
Analysis
Question Analysis:
This question tests the understanding that only the shorter diagonal is bisected in a kite.
It also requires applying the Pythagorean Theorem using legs from unequal halves of the diagonals.
Key Concept Explanation:
In a kite, the longer diagonal is not bisected, only the shorter diagonal is.
When two diagonals intersect at 90°, they form right triangles, and a kite side can be the hypotenuse.
Step-by-Step Solution:
Given:
- AE = 8 cm (not half of AC)
- BE = 6 cm (half of BD)
Triangle ABE has legs 8 and 6, with AB as hypotenuse
Use Pythagorean Theorem:
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