Question

The diagonal of a square is x units. What is the area of the square in terms of x?

Answer 1

Answer:

1/2(x²) square units

Step-by-step explanation

From the question,

Area of a Square(A) = L²

A = L²................. Equation 1

Where L = Lenght of the square

If the diagonal of the square is x,

Using pythagoras theorem,

a² = b²+c².................. Equation 2

Wherer a = x, b = c= L

Therefore,

x² = L²+L²

x² = 2L²

L² = x²/2

L = √(x²/2)

Substitute the value of L into equation 1

A = [√(x²/2)]²

A = x²/2 square unit.

A = 1/2(x²) square unit.

The right option is 1/2(x²) square units