Question

What would be the length of side BC in Square ABCD if the diagonal of the square given is 10 cm?
A. $ 5 $
B.\[5\sqrt 2 \]
C. $ 10 $
D. $ 10\sqrt 2 $

Answer 1

Hint: To answer this type of question we need to know the relation between the side length and the diagonal length of the square . In this question already the length of the diagonal is given so by using the relation between the side and the diagonal we can find the length of the side of the square ABCD.

Complete step-by-step answer:
Suppose a square ABCD is given as shown in figure

As we can see the length of the diagonal in square ABCD is
\[AC = 10{\text{ }}cm\]
We know that the diagonal of a square is always equal to $ \sqrt 2 a $
Here the value of diagonal is given that means
 $ \sqrt 2 a = 10 $ is given.
We need to find the value of “a” which will be equal to the all side length.
So if $ \sqrt 2 a = 10 $
Then,
 $ a = \dfrac{{10}}{{\sqrt 2 }} $
Or we can write it like
 $
\Rightarrow a = \dfrac{{10}}{{\sqrt 2 }} \\
\Rightarrow a = \dfrac{{2 \times 5}}{{\sqrt 2 }} \\
\Rightarrow a = 5\sqrt 2 \;
 $
Here \[a = AB = BC = CD = AD = 5\sqrt 2 \]
Hence the length of side BC = \[5\sqrt 2 \]cm
So, the correct answer is “Option B”.

Note: In a square there are two diagonals having the same length and intersect perpendicularly. While Rhombus has also all sides having the same length but different length of diagonal.