Question

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

Answer 1

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.

Answer 2

"The length of the diagonal is $\left( (x+5)\sqrt { 2 } \right) \quad cm$

Given:

The "perimeter of a square" is (4x + 20) cm

To find:

Length of its diagonal.

Solution:

$Perimeter\quad of\quad a\quad square\quad =\quad 4\quad \times \quad side$

$4x\quad +\quad 20\quad =\quad side\quad \times \quad 4$

$side\quad =\quad \frac{4 x+20}{4}$

$side\quad =\quad \frac { 4\left( x+5 \right) }{ 4 }$

$\therefore \quad side\quad =\quad x+5\quad cm$

Now,

"Diagonal of a square" $= \sqrt { 2 } \quad \times \quad length\quad of\quad the\quad side$

$Diagonal\quad =\quad \left( (x+5)\sqrt { 2 } \right) \quad cm$"