Question

The given square has a diagonal of 24 meters. What is the measure of a side length? Round to the nearest tenth, if necessary

Answer 1

Answer:

     Side of the square ≅ $16.97$

Step-by-step explanation:

The diagonal of a square with side 'a' makes right angled Isosceles triangle.

The Diagonal becomes hypotenuse of the triangle i.e 24 m (given)

Using Pythagorean Theorem:

$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$

As, Perpendicular and base of the triangle is equal in case of a square with a side of 'a'

                        $H^2=a^2+a^2\\\\24^2=2a^2\\\\2a^2=576\\\\a^2=288\\\\a=\sqrt{288}$≅ $16.97$

OR, (Alternate method)

        Diagonal of a square = $\sqrt{2}*a$

                                                                                   :  $\sqrt{2} =1.414$

                                    $24=\sqrt{2}*a\\\\ 24=1.414*a\\\\a=\frac{24}{1.414} \\\\a=16.973$