Find the area and the perimeter of a square room , the length of whose diagonal is 15 cm . Give your answer to three significant figures.

The correct answer is: ∴ Perimeter and Area of the given square is 4 √112.5 cm or 42.4 cm & 112.5 cm2, respectively.

Step-by-step solution:-
In the adjacent diagram, we can see that the diagonal divides the given square into 2 right angled triangles.
Also, diagonal of the square becomes the hypotenuse of the 2 triangles.
Hypotenuse of the given triangles = diagonal of the given square = 15 cm
Let the sides of the given square be x cm.
∴ side of the triangles (other than hypotenuse) = x cm.
By applying Pythagorean theorem, For a right angled triangle-
Hypotenuse² = sum of the squares of the remaining 2 sides
∴  (15)2 = x² + x²
∴  225 = 2x²
∴  225 / 2 = x²
∴  x² = 112.5
∴  x = √112.5 .............................. (Taking square root both the sides) ........................ (Equation i)
Perimeter of the given square = 4 × side
∴ Perimeter of the given square = 4 × x
∴ Perimeter of the given square = 4 × √112.5 cm or 42.4 cm........................................................................ (From Equation i)
Area of the given square = side²
∴ Area of the given square = (√112.5)² ............................................................................................................. (From Equation i)
∴ Area of the given square = 112.5 cm²
Final Answer:-
∴ Perimeter and Area of the given square is 4 √112.5 cm or 42.4 cm & 112.5 cm², respectively.