Question

The figure shown above consists a of square $BCDE$ and an equilateral triangle $\Delta ABE$. The length of $\overline{CD}$ is $6$ inches. Calculate the perimeter of $ABCDE$ in inches.

• A. 18
• B. 24
• C. 30
• D. 42
• E. 45

Answer 1

The correct option is C 30

Consider $BE$ as the base of the equilateral triangle$ABE$.

Now, since $EBCD$ is a square, $BE=BC=CD=DE=6$.

Thus $BE=6$

But, $ABE$ is an equilateral triangle.

Hence $AB=BE=AE=6$.
Hence, the perimeter of the above figure is $AB+BC+CD+DE+EA=5\times 6=30$.