Question

The diagonal of a square is 19 root 2 cm. Find its area and perimeter

Answer 1

Answer:

PERIMETER = 76 cm

AREA = 361 cm²

Step-by-step explanation:

Let the side of the square be a.

In a  square the diagonal and adjacent sides form a right angled triangle.        

in that right angled triangle the lengths of the two perpendicular legs = a;

The length of the hypotenuse = The length of the diagonal = d;

Using Pythagoras theorem,

Hyp² = side1² + side2²

d²     = a² + a²

d²     = 2a²

d      = a√2

given the length of the diagonal = d = 19√2 cm

d= 19√2 = a√2

⇒ a = 19cm

The perimeter of a square = 4×(length of the side)    = 4a    = 4×19= 76

Area of a square = side×side = a×a = 19×19 = 361 cm²