Question

perimeter
what is the perimeter of the following squares?

1. 121 units²
2. 45 units²
3. 72 units²
4. 19 units²

Explanation:

Step1: Recall square - area formula

The area formula of a square is $A = s^{2}$, where $A$ is the area and $s$ is the side - length.

Step2: Find side - length for each square

For square 1:

Given $A_1=121$ units². Since $A_1 = s_1^{2}$, then $s_1=\sqrt{121}=11$ units. The perimeter of a square is $P = 4s$, so $P_1 = 4\times11 = 44$ units.

For square 2:

Given $A_2 = 45$ units². Then $s_2=\sqrt{45}=3\sqrt{5}$ units. The perimeter $P_2=4s_2 = 4\times3\sqrt{5}=12\sqrt{5}$ units.

For square 3:

Given $A_3 = 72$ units². Then $s_3=\sqrt{72}=6\sqrt{2}$ units. The perimeter $P_3=4s_3=4\times6\sqrt{2}=24\sqrt{2}$ units.

For square 4:

Given $A_4 = 19$ units². Then $s_4=\sqrt{19}$ units. The perimeter $P_4=4s_4 = 4\sqrt{19}$ units.

Answer:

1. 44 units
2. $12\sqrt{5}$ units
3. $24\sqrt{2}$ units
4. $4\sqrt{19}$ units