Question

Find the area of a square the length of whose diagonal is 25 centimetre​

Answer 1

Answer:

Diagonal =Length

Length 25 cm

Perimeter =25×4 =100 cm

Answer 2

Answer:

• Area of square is 312.5 cm².

Step-by-step explanation:

Here,

Concept is first we will find the side of square for area.

Let, Square be ABCD.

And Diagonals be AC of measure 25 cm.

• We know all sides of square are equal and parallel.

So,

AB = BC = x

• All angles of square are 90°.

So, Angle B is off 90°.

Thus,

∆ABC is right angle triangle.

We will use Pythagoras theorem that is:

• Pythagoras theorem is the theorem which states that square of hypotenuse is equal to the sum of squares of the other two sides of right angle triangle.
• Hypotenuse is the longest side of right angle triangle. This side is opposite to 90° angle.
• This Pythagoras theorem is written in formula as: Hypotenuse² = Base² + Perpendicular²

Now,

Perpendicular = x

Base = x

Hypotenuse = AB = 25 cm.

Put all values in Pythagoras theorem :

$\longrightarrow$ (25)² = (x)² + (x)²

$\longrightarrow$ 625 = x² + x²

$\longrightarrow$ 625 = 2x²

$\longrightarrow$ x² = 625/2

$\longrightarrow$ x² = 312.5

$\longrightarrow$ x = √312.5

$\longrightarrow$ x = 17.67

x is side of square.

So, Measure of one side of square is 17.67 cm.

We know,

Area of square = Side × Side

$\longrightarrow$ 17.67 × 17.67

$\longrightarrow$ 312.5

Therefore,

Area of square is 312.5 cm².