Question

A square has a diagonal that measures $6$ inches.

Which of the following is the length of its perimeter?

• A. $\frac{8}{3}inches$
• B. $1272inches$
• C. $673\mathrm{inches}$
• D. $1872\mathrm{inches}$
• E. None of these

Answer 1

The correct option is E

None of these

The explanation for the correct option (E):

The length of the diagonal is $6\mathrm{inches}$.

Let $x$ be the edge of the square,

so, the diagonal will be $\sqrt{2}x$.

Calculate the value of $x$ as shown:

$$\begin{gathered} \sqrt{2}x=6 \\ x=\frac{6}{\sqrt{2}} \\ =\frac{6}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}} \\ =3\sqrt{2} \end{gathered}$$

Now, calculate the perimeter of the square as follows:

$$\begin{gathered} \mathrm{Perimeter}=4\times \mathrm{edge}\mathrm{of}\mathrm{square} \\ =4\times 3\sqrt{2} \\ =12\sqrt{2} \\ =16.97\mathrm{inches} \end{gathered}$$

Hence, option (E) is correct.

The explanation for the incorrect options:

Since the perimeter of a square is not equal to any of the options given above, hence option(A), option(B), option (C), and option(D) are incorrect.