Question

#3 which square has a side length closest to 12 centimeters? a. a square with an area of 160 cm² b. a square with an area of 48 cm² c. a square with an area of 150 cm² d. a square with an area of 3 cm²

Explanation:

Step1: Recall the formula for the area of a square

The area formula of a square is \(A = s^{2}\), where \(s\) is the side - length. Then \(s=\sqrt{A}\).

Step2: Calculate the side - length for each option

• For option A: If \(A = 160\space cm^{2}\), then \(s=\sqrt{160}\approx12.65\space cm\) (since \(12.65^{2}=160\)).
• For option B: If \(A = 48\space cm^{2}\), then \(s=\sqrt{48}\approx6.93\space cm\) (since \(6.93^{2}\approx48\)).
• For option C: If \(A = 150\space cm^{2}\), then \(s=\sqrt{150}\approx12.25\space cm\) (since \(12.25^{2}=150.0625\approx150\)).
• For option D: If \(A = 3\space cm^{2}\), then \(s=\sqrt{3}\approx1.73\space cm\) (since \(1.73^{2}\approx3\)).

Step3: Compare the side - lengths to 12 cm

Calculate the absolute differences:

• \(|12.65 - 12|=0.65\)
• \(|6.93 - 12| = 5.07\)
• \(|12.25 - 12|=0.25\)
• \(|1.73 - 12|=10.27\)

Since \(0.25\lt0.65\lt5.07\lt10.27\)

Answer:

C. A square with an area of \(150\space cm^{2}\)