Question

a. if the area of a square is 729 cm², what is its perimeter? b. if the perimeter of a square is 56 cm, what is its area? a. the perimeter of the square is b. the area of the square is

Explanation:

Part a

Step1: Find the side length of the square

The area formula of a square is \(A = s^{2}\), where \(A\) is the area and \(s\) is the side - length. Given \(A = 729\space cm^{2}\), then \(s=\sqrt{729}\).
Since \(27\times27 = 729\), so \(s = 27\space cm\).

Step2: Calculate the perimeter of the square

The perimeter formula of a square is \(P=4s\). Substitute \(s = 27\space cm\) into the formula, we get \(P = 4\times27\).
\(P=108\space cm\).

Part b

Step1: Find the side length of the square

The perimeter formula of a square is \(P = 4s\), where \(P\) is the perimeter and \(s\) is the side - length. Given \(P = 56\space cm\), then \(s=\frac{P}{4}\).
Substitute \(P = 56\space cm\) into the formula, \(s=\frac{56}{4}=14\space cm\).

Step2: Calculate the area of the square

The area formula of a square is \(A = s^{2}\). Substitute \(s = 14\space cm\) into the formula, we get \(A=14^{2}\).
\(A = 196\space cm^{2}\).

Answer:

a. \(108\space cm\)
b. \(196\space cm^{2}\)