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What is the estimated length of the diagonal of a square with an area of 100 cm², using the formula d = 1.4x^(1/2)?

A. 11.8 cm
B. 14.1 cm
C. 17.3 cm
D. 20.0 cm

1 Answer

4 votes

Final answer:

The estimated length of the diagonal of a square with an area of 100 cm² is found by first determining the side length and then using the formula d = 1.4·(side length)⁻½, resulting in an estimated diagonal of approximately 14.1 cm.

Step-by-step explanation:

The question asks for the estimated length of the diagonal of a square with an area of 100 cm², using the formula d = 1.4x⁻½. To find the length of a square's diagonal when the area is known, we first need to determine the side length of the square. Since the area of a square is found using the formula side length squared, we can find the side length by taking the square root of the area. In this case, the side length is √(100 cm²) which equals 10 cm. We then apply the formula for the diagonal:

d = 1.4 × (side length)⁻½

By substituting in the side length (10 cm), we get:

d = 1.4 × (10 cm)⁻½ =

d = 1.4 × (10¹⁻½) =

d = 1.4 × 3.16 cm ≈ 14.1 cm

Hence, the answer is B. 14.1 cm.

User Oleg Bogdanov
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