Question

the diagonal of a square is 12 cm long find its area and length of one side​

Answer 1

Answer:

Length of one side = 8.5 cm

Area = 72.25 sq cm

Explanation:

Since all sides of a square are equal

Let length of a side be x

Let Quadrilateral ABCD is a square

AC is the diagonal

Therefore AC = 12 cm

In triangle ABC , (AC)^2 = (AB)^2 + (BC)^2

(AC)^2 = x^2 + x^2 (since all sides are equal)

(AC)^2 = 2x^2

Squarring on both sides

AC = root2x

12 = root2x

Therefore x = 12/root2 = 8.5 cm

Therefore length of one side is 8.5 cm

Now Area = x^2 = 8.5^2 = 8.5*8.5 = 72.25 sq cm

Therefore area of the square is 72.25 sq cm