. Diagonal AC of a rectangle ABCD is produced to the point E such that AC : CE = 2 :1, AB = 16 cm and BC = 12 cm. Find the length of DE.
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Answer:
The diagonal of a rectangle can be found using the hypotenuse theorem.
⇒AC
2
=AB
2
+BC
2
⇒(2x
2
)=8
2
+6
2
4x
2
=64+36
⇒x
2
=25
∴x=5cm
∴AC=10cm and CE=5cm
From the figure know that AE=15cm,AD=6cm
△DEA is a right angle triangle.
∴DE=
15
2
−6
2
=12.36≅3
17
.
Hence, the answer is 3
17
.
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