Question

Diagonal AC of a rectangle ABCD is produced to the point E such that AC : CE =$2:1$, AB =$8$ cm and BC = $6$ cm. Find the length of DE (in cm)

• A. $\sqrt{17}$
• B. $3\sqrt{17}$
• C. $2\sqrt{17}$
• D. $4\sqrt{17}$

Answer 1

The correct option is B $3\sqrt{17}$

The diagonal of a rectangle can be found using the hypotenuse theorem.

$\Rightarrow A{C}^2=A{B}^2+B{C}^2$

$\Rightarrow \left(2x^2\right)=8^2+6^2$

$4x^2=64+36$

$\Rightarrow x^2=25$

$\therefore x=5$cm

$\therefore AC=10cm$ and $CE=5cm$

From the figure know that $AE=15cm,AD=6cm$

$△DEA$ is a right angle triangle.

$\therefore DE=\sqrt{{15}^2-6^2}$

$=12.36\cong 3\sqrt{17}.$

Hence, the answer is $3\sqrt{17}.$