Question

find the perimeter of a square if it's diagonal is 10✓2​

Answer 1

40 units

According to the information provided in the given question, we have:

• The diagonal of a square is given as 10√2 units.

We've been asked to calculate the perimeter of the square.

ー We know, the diagonal of a square is square root of 2 multiplied by side of square. Here, let's take side of square as a. Therefore, the formula is given as:

$\qquad\qquad\star~{\underline{\boxed{\pmb{\frak{Diagonal\; of\; square=\sqrt{2}\times a}}}}}$

Now, let's equate the value of diagonal of square in the formula.

$\\:\implies\quad\sf{10\sqrt{2}=\sqrt{2}\times a}$

$\\\\:\implies\quad\sf{\dfrac{10\sqrt{2}}{\sqrt{2}}=a}$

$\\\\:\implies\quad\pmb{\sf{a=10\; units}}$

Now, let's equate this value in perimeter of square formula.

★ Perimeter of square is defined as four times the side of square. Let's take perimeter of square as P here.

$\\\dashrightarrow\quad\sf{P=4\times a}$

$\\\\\dashrightarrow\quad\sf{P=4\times 10}$

$\\\\\dashrightarrow\quad\underline{\boxed{\pmb{\frak{\purple{P=40\; units}}}}}$

❝Henceforth, the perimeter of square is 40 units.❞