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

Question

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

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2 days 2021-10-12T11:21:22+00:00 2 Answers 0

The side of the square = x/√2

Step-by-step explanation:

All the sides of a square are equal. All the angles are equal to 90°

To find the side of a square

From the figure attached with this answer shows a square.

Let ‘x’ be the diagonal of the square.

The diagonal make two right angled triangle with angle 45°, 45° and 90°

Therefore the sides are in the ratio 1 : 1 : √2

Here diagonal = x

side : side : x= side : side : √2

Therefore one side length = x/√2

Area = x²/2 square units

Step-by-step explanation:

The key to solving this question is to understand that:

a) the sides of a square are the same length

b) the length of the diagonal may be calculated via Pythagoras’ theorem (c² = a² + b², where c is the length of the hypotenuse of a triangle and a and b the lengths of the other two sides)

1. Now, let’s call the sides of the square length y and the diagonal is length x.

Using c² = a² + b², we can substitute our values to get:

x² = y² + y²

x² = 2y²

2. Stepping away from Pythagoras’ theorem for a little bit, let us think of the general formula for the area of a square:

A (for Area) = a², where a is the length of the sides of the square (which are all of equal length)

Given that we defined our square as having length y, let us substitute this value in to get:

A = y²

3. Now we have two formulas that we can work with:

1) x² = 2y²

2) A = y²

4. Given that A = y², we can say that 2y² = 2A

Therefor, if x² = 2y², then x² = 2A

Thus, if we want to find the formula for area in terms of x, we need to simply rearrange the given formula to make A the subject, giving us:

A = x²/2 square units

Hope that helps 🙂