The quadrilateral shown is a rhombus. If AB = 17 and AE = 8, what is the measure of BE? A) 11 B) 13 C) 15 D) 19
Answers
If AB = 17 and AE = 8, then the measure of BE is option (C): 15.
Step-by-step explanation:
Referring to the figure attached below, we have
ABCD is a rhombus with the diagonals intersecting at E
Each side of a rhombus, AB = BC = CD = DA = 17
The measure of AE = 8
We know that the diagonals of a rhombus bisect each other at right angles.
∴ ∠AEB = ∠BEC = ∠CED = ∠DEA = 90°
Now, considering ∆ AEB and applying Pythagoras theorem, we get
AB² = AE² + BE²
⇒ BE = √[AB² – AE²]
⇒ BE = √[17² – 8²]
⇒ BE = √[225]
⇒ BE = 15
Thus, the measure of the BE is 15.
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