Question

The midpoint of the diagonal of a a square is 4 units from the vertex of the square. Calculate

(a) the perimeter of the square.
(b) the area of the square.​

Answer 1

Below in bold.

Explanation:

Let the sides of the square be x units long.

The length of the diagonal = 2*4 = 8 units ( as the midpoint is 4 from vertex).

By Pythagoras:

x^2 + x^2 = 8^2

Solving for x:

2x^2 = 64

x^2 = 32

x = √32

= 4√2.

(a) Perimeter = 4 * 4√2

= 16√2 units.

(b) Area = (4√2)^2

= 16 * 2

= 32 units.