Question

The perimeter of a square is (4x+20)cm. What will be the length of its diagonal?​

Answer 1

Answer:

Perimeter of a square = 4 * side

4x + 20 = side * 4

side = 4x + 20 / 4

side = 4 ( x + 5 ) / 4

∴side = x + 5 cm.

Now,

Diagonal of a square = √2 * side

Diagonal = √2 * ( x + 5 ) cm.

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Answer 2

We have,

Perimeter of square = (4x + 20) cm

Let one side be = s

∵ Perimeter of square = 4 × side,

∴ 4s = 4x + 20

⇒4s = 4(x + 5)

By cancelling 4 on both the sides,

⇒s = (x + 5) cm

Now we know, diagonal of a square = s√2 {Find through Pythagoras theorem if you do not know}

∴ Diagonal = (x + 5)√2 = (x√2 + 5√2) cm {Answer}