Question

If the perimeter of a square is (4y + 12) m, then the length of its diagonal is

• A. $\frac{y+3}{\sqrt{2}}m$
• B. $\sqrt{2}(y+3)m$
• C. $\sqrt{2}(4y+12)m$
• D. $\frac{4y+12}{\sqrt{2}}m$

Answer 1

Answer: (B)

$\sqrt{2}(y+3)m$

Consider the given perimeter of the square is $=(4y+12)$m.

We know, perimeter of the square =$4\times$ side

$(4y+12)$=$4\times$ side.

Side$=\frac{4y+12}{4}=y+3$

Now, length of diagonal of the square

$=\sqrt{{\left(side\right)}^2+{\left(side\right)}^2}$

$=\sqrt{{(y+3)}^2+{(y+3)}^2}$

$=\sqrt{2}.(y+3)m$